diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
index a00f93baf..91e0889e9 100644
--- a/.gitlab-ci.yml
+++ b/.gitlab-ci.yml
@@ -6,7 +6,7 @@ tests:
         - virtualenv-3.4 env
         - source env/bin/activate
         - cd src
-        - XDG_CACHE_HOME=/cache pip3 install -r requirements.txt -r requirements/dev.txt
+        - XDG_CACHE_HOME=/cache pip3 install -r requirements.txt -r requirements/dev.txt -r requirements/py34.txt
         - flake8 --ignore=E123,F403,F401,N802,C901,W503 .
         - isort -c -rc .
         - python3 manage.py check
diff --git a/.travis.yml b/.travis.yml
index f75905c33..4400f6d00 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -4,7 +4,7 @@ python:
     - "3.4"
 install:
     - pip install -U pip wheel
-    - pip install -q -r src/requirements.txt -r src/requirements/dev.txt
+    - pip install -q -r src/requirements.txt -r src/requirements/dev.txt -r src/requirements/py34.txt
     - npm install -g less@2.5.0
 before_script:
     - cd src
diff --git a/deployment/docker/standalone/Dockerfile b/deployment/docker/standalone/Dockerfile
index 1ecd4aef9..cd1a932d1 100644
--- a/deployment/docker/standalone/Dockerfile
+++ b/deployment/docker/standalone/Dockerfile
@@ -23,7 +23,8 @@ RUN git clone --recursive --depth 1 https://github.com/pretix/pretix.git /pretix
 WORKDIR /pretix/src
 
 RUN pip3 install -r requirements.txt -r requirements/mysql.txt -r requirements/postgres.txt \
-	-r requirements/memcached.txt -r requirements/celery.txt -r requirements/redis.txt gunicorn
+	-r requirements/memcached.txt -r requirements/celery.txt -r requirements/redis.txt \
+	-r requirements/py34.txt gunicorn
 
 RUN make
 
diff --git a/src/pretix/base/cache.py b/src/pretix/base/cache.py
index c913a13bb..e61915f73 100644
--- a/src/pretix/base/cache.py
+++ b/src/pretix/base/cache.py
@@ -3,11 +3,12 @@ import time
 
 from django.core.cache import caches
 from django.db.models import Model
+from typing import Dict, List
 
 
 class NamespacedCache:
 
-    def __init__(self, prefixkey, cache: str='default'):
+    def __init__(self, prefixkey: str, cache: str='default'):
         self.cache = caches[cache]
         self.prefixkey = prefixkey
 
@@ -30,7 +31,7 @@ class NamespacedCache:
     def _strip_prefix(self, key: str) -> str:
         return key.split(":", 2 + self.prefixkey.count(":"))[-1]
 
-    def clear(self):
+    def clear(self) -> None:
         try:
             prefix = self.cache.incr(self.prefixkey, 1)
         except ValueError:
@@ -43,14 +44,14 @@ class NamespacedCache:
     def get(self, key: str) -> str:
         return self.cache.get(self._prefix_key(key))
 
-    def get_many(self, keys: "list[str]") -> "dict[str, str]":
+    def get_many(self, keys: List[str]) -> Dict[str, str]:
         values = self.cache.get_many([self._prefix_key(key) for key in keys])
         newvalues = {}
         for k, v in values.items():
             newvalues[self._strip_prefix(k)] = v
         return newvalues
 
-    def set_many(self, values: "dict[str, str]", timeout=3600):
+    def set_many(self, values: Dict[str, str], timeout=3600):
         newvalues = {}
         for k, v in values.items():
             newvalues[self._prefix_key(k)] = v
@@ -59,7 +60,7 @@ class NamespacedCache:
     def delete(self, key: str):  # NOQA
         return self.cache.delete(self._prefix_key(key))
 
-    def delete_many(self, keys: "list[str]"):  # NOQA
+    def delete_many(self, keys: List[str]):  # NOQA
         return self.cache.delete_many([self._prefix_key(key) for key in keys])
 
     def incr(self, key: str, by: int=1):  # NOQA
@@ -86,6 +87,6 @@ class ObjectRelatedCache(NamespacedCache):
     times as you want.
     """
 
-    def __init__(self, obj, cache: str='default'):
+    def __init__(self, obj: Model, cache: str='default'):
         assert isinstance(obj, Model)
         super().__init__('%s:%s' % (obj._meta.object_name, obj.pk), cache)
diff --git a/src/pretix/base/exporter.py b/src/pretix/base/exporter.py
index 1b081009d..2be7444d3 100644
--- a/src/pretix/base/exporter.py
+++ b/src/pretix/base/exporter.py
@@ -2,6 +2,7 @@ import json
 
 from django.core.serializers.json import DjangoJSONEncoder
 from django.dispatch import receiver
+from typing import Tuple
 
 from pretix.base.signals import register_data_exporters
 
@@ -60,7 +61,7 @@ class BaseExporter:
         """
         return {}
 
-    def render(self, form_data: dict) -> tuple:
+    def render(self, form_data: dict) -> Tuple[str, str, str]:
         """
         Render the exported file and return a tuple consisting of a filename, a file type
         and file content.
diff --git a/src/pretix/base/forms/auth.py b/src/pretix/base/forms/auth.py
index f3c96dfcf..d5ec586b5 100644
--- a/src/pretix/base/forms/auth.py
+++ b/src/pretix/base/forms/auth.py
@@ -43,7 +43,7 @@ class LoginForm(forms.Form):
 
         return self.cleaned_data
 
-    def confirm_login_allowed(self, user):
+    def confirm_login_allowed(self, user: User):
         """
         Controls whether the given User may log in. This is a policy setting,
         independent of end-user authentication. This default behavior is to
diff --git a/src/pretix/base/i18n.py b/src/pretix/base/i18n.py
index fdca837d3..f4d82e71f 100644
--- a/src/pretix/base/i18n.py
+++ b/src/pretix/base/i18n.py
@@ -6,6 +6,7 @@ from django.conf import settings
 from django.db.models import SubfieldBase, TextField
 from django.utils import translation
 from django.utils.safestring import mark_safe
+from typing import Dict, List
 
 
 class LazyI18nString:
@@ -13,7 +14,7 @@ class LazyI18nString:
     This represents an internationalized string that is/was/will be stored in the database.
     """
 
-    def __init__(self, data):
+    def __init__(self, data: Dict[str, str]):
         """
         Input data should be a dictionary which maps language codes to content.
         """
@@ -26,7 +27,7 @@ class LazyI18nString:
             else:
                 self.data = j
 
-    def __str__(self):
+    def __str__(self) -> str:
         """
         Evaluate the given string with respect to the currently active locale.
         This will rather return you a string in a wrong language than give you an
@@ -53,10 +54,10 @@ class LazyI18nString:
         else:
             return str(self.data)
 
-    def __repr__(self):
+    def __repr__(self) -> str:
         return '<LazyI18nString: %s>' % repr(self.data)
 
-    def __lt__(self, other):  # NOQA
+    def __lt__(self, other) -> bool:  # NOQA
         return str(self) < str(other)
 
 
@@ -68,7 +69,7 @@ class I18nWidget(forms.MultiWidget):
     """
     widget = forms.TextInput
 
-    def __init__(self, langcodes, field, attrs=None):
+    def __init__(self, langcodes: List[str], field: forms.Field, attrs=None):
         widgets = []
         self.langcodes = langcodes
         self.enabled_langcodes = langcodes
diff --git a/src/pretix/base/middleware.py b/src/pretix/base/middleware.py
index 55b2756d0..580eaeadd 100644
--- a/src/pretix/base/middleware.py
+++ b/src/pretix/base/middleware.py
@@ -3,6 +3,7 @@ from collections import OrderedDict
 import pytz
 from django.conf import settings
 from django.core.urlresolvers import get_script_prefix
+from django.http import HttpRequest, HttpResponse
 from django.utils import timezone, translation
 from django.utils.cache import patch_vary_headers
 from django.utils.translation import LANGUAGE_SESSION_KEY
@@ -21,7 +22,7 @@ class LocaleMiddleware:
     for a request.
     """
 
-    def process_request(self, request):
+    def process_request(self, request: HttpRequest):
         language = get_language_from_request(request)
         if hasattr(request, 'event') and not request.path.startswith(get_script_prefix() + 'control'):
             if language not in request.event.settings.locales:
@@ -51,7 +52,7 @@ class LocaleMiddleware:
         else:
             timezone.deactivate()
 
-    def process_response(self, request, response):
+    def process_response(self, request: HttpRequest, response: HttpResponse):
         language = translation.get_language()
         patch_vary_headers(response, ('Accept-Language',))
         if 'Content-Language' not in response:
@@ -59,14 +60,14 @@ class LocaleMiddleware:
         return response
 
 
-def get_language_from_user_settings(request) -> str:
+def get_language_from_user_settings(request: HttpRequest) -> str:
     if request.user.is_authenticated():
         lang_code = request.user.locale
         if lang_code in _supported and lang_code is not None and check_for_language(lang_code):
             return lang_code
 
 
-def get_language_from_session_or_cookie(request) -> str:
+def get_language_from_session_or_cookie(request: HttpRequest) -> str:
     if hasattr(request, 'session'):
         lang_code = request.session.get(LANGUAGE_SESSION_KEY)
         if lang_code in _supported and lang_code is not None and check_for_language(lang_code):
@@ -79,7 +80,7 @@ def get_language_from_session_or_cookie(request) -> str:
         pass
 
 
-def get_language_from_event(request) -> str:
+def get_language_from_event(request: HttpRequest) -> str:
     if hasattr(request, 'event'):
         lang_code = request.event.settings.locale
         try:
@@ -88,7 +89,7 @@ def get_language_from_event(request) -> str:
             pass
 
 
-def get_language_from_browser(request) -> str:
+def get_language_from_browser(request: HttpRequest) -> str:
     accept = request.META.get('HTTP_ACCEPT_LANGUAGE', '')
     for accept_lang, unused in parse_accept_lang_header(accept):
         if accept_lang == '*':
@@ -110,7 +111,7 @@ def get_default_language():
         return settings.LANGUAGE_CODE
 
 
-def get_language_from_request(request) -> str:
+def get_language_from_request(request: HttpRequest) -> str:
     """
     Analyzes the request to find what language the user wants the system to
     show. Only languages listed in settings.LANGUAGES are taken into account.
diff --git a/src/pretix/base/migrations/0004_auto_20151024_0848.py b/src/pretix/base/migrations/0004_auto_20151024_0848.py
index 5d12fd750..50d566d44 100644
--- a/src/pretix/base/migrations/0004_auto_20151024_0848.py
+++ b/src/pretix/base/migrations/0004_auto_20151024_0848.py
@@ -1,7 +1,7 @@
 # -*- coding: utf-8 -*-
 from __future__ import unicode_literals
 
-from django.db import models, migrations
+from django.db import migrations, models
 
 
 class Migration(migrations.Migration):
diff --git a/src/pretix/base/models/auth.py b/src/pretix/base/models/auth.py
index b3e1ef6c8..aef87c5d6 100644
--- a/src/pretix/base/models/auth.py
+++ b/src/pretix/base/models/auth.py
@@ -12,13 +12,13 @@ class UserManager(BaseUserManager):
     model documentation to see what's so special about our user model.
     """
 
-    def create_user(self, email, password=None, **kwargs):
+    def create_user(self, email: str, password: str=None, **kwargs):
         user = self.model(email=email, **kwargs)
         user.set_password(password)
         user.save()
         return user
 
-    def create_superuser(self, email, password=None):  # NOQA
+    def create_superuser(self, email: str, password: str=None):  # NOQA
         # Not used in the software but required by Django
         if password is None:
             raise Exception("You must provide a password")
diff --git a/src/pretix/base/models/base.py b/src/pretix/base/models/base.py
index 6302df8d5..9dfc0fd4e 100644
--- a/src/pretix/base/models/base.py
+++ b/src/pretix/base/models/base.py
@@ -1,5 +1,6 @@
 import copy
 import uuid
+from datetime import datetime
 
 import six
 from django.db import models
@@ -12,7 +13,7 @@ class Versionable(BaseVersionable):
     class Meta:
         abstract = True
 
-    def clone_shallow(self, forced_version_date=None):
+    def clone_shallow(self, forced_version_date: datetime=None):
         """
         This behaves like clone(), but misses all the Many2Many-relation-handling. This is
         a performance optimization for cases in which we have to handle the Many2Many relations
@@ -63,7 +64,7 @@ class Versionable(BaseVersionable):
         })
 
 
-def cachedfile_name(instance, filename):
+def cachedfile_name(instance, filename: str) -> str:
     return 'cachedfiles/%s.%s' % (instance.id, filename.split('.')[-1])
 
 
diff --git a/src/pretix/base/models/items.py b/src/pretix/base/models/items.py
index 0eeabbecd..e55b2575c 100644
--- a/src/pretix/base/models/items.py
+++ b/src/pretix/base/models/items.py
@@ -1,4 +1,6 @@
 import sys
+from datetime import datetime
+from decimal import Decimal
 from itertools import product
 
 from django.db import models
@@ -6,6 +8,7 @@ from django.db.models import Q, Case, Count, Sum, When
 from django.utils.functional import cached_property
 from django.utils.timezone import now
 from django.utils.translation import ugettext_lazy as _
+from typing import List, Tuple, Union
 from versions.models import VersionedForeignKey, VersionedManyToManyField
 
 from pretix.base.i18n import I18nCharField, I18nTextField
@@ -61,11 +64,11 @@ class ItemCategory(Versionable):
     def sortkey(self):
         return self.position, self.version_birth_date
 
-    def __lt__(self, other):
+    def __lt__(self, other) -> bool:
         return self.sortkey < other.sortkey
 
 
-def itempicture_upload_to(instance, filename):
+def itempicture_upload_to(instance, filename: str) -> str:
     return '%s/%s/item-%s.%s' % (
         instance.event.organizer.slug, instance.event.slug, instance.identity,
         filename.split('.')[-1]
@@ -170,7 +173,7 @@ class Item(Versionable):
         if self.event:
             self.event.get_cache().clear()
 
-    def get_all_variations(self, use_cache: bool=False) -> "list[VariationDict]":
+    def get_all_variations(self, use_cache: bool=False) -> List[VariationDict]:
         """
         This method returns a list containing all variations of this
         item. The list contains one VariationDict per variation, where
@@ -438,10 +441,10 @@ class PropertyValue(Versionable):
             self.prop.event.get_cache().clear()
 
     @property
-    def sortkey(self):
+    def sortkey(self) -> Tuple[int, datetime]:
         return self.position, self.version_birth_date
 
-    def __lt__(self, other):
+    def __lt__(self, other) -> bool:
         return self.sortkey < other.sortkey
 
 
@@ -508,7 +511,7 @@ class ItemVariation(Versionable):
         if self.item:
             self.item.event.get_cache().clear()
 
-    def check_quotas(self):
+    def check_quotas(self) -> Tuple[int, int]:
         """
         This method is used to determine whether this ItemVariation is currently
         available for sale in terms of quotas.
@@ -518,7 +521,7 @@ class ItemVariation(Versionable):
         return min([q.availability() for q in self.quotas.all()],
                    key=lambda s: (s[0], s[1] if s[1] is not None else sys.maxsize))
 
-    def to_variation_dict(self):
+    def to_variation_dict(self) -> VariationDict:
         """
         :return: a :py:class:`VariationDict` representing this variation.
         """
@@ -528,7 +531,7 @@ class ItemVariation(Versionable):
         vd['variation'] = self
         return vd
 
-    def check_restrictions(self):
+    def check_restrictions(self) -> Union[bool, Decimal]:
         """
         This method is used to determine whether this ItemVariation is restricted
         in sale by any restriction plugins.
@@ -806,7 +809,7 @@ class Quota(Versionable):
         if self.event:
             self.event.get_cache().clear()
 
-    def availability(self):
+    def availability(self) -> Tuple[int, int]:
         """
         This method is used to determine whether Items or ItemVariations belonging
         to this quota should currently be available for sale.
@@ -864,7 +867,7 @@ class Quota(Versionable):
         return o
 
     @cached_property
-    def _position_lookup(self):
+    def _position_lookup(self) -> Q:
         return (
             (  # Orders for items which do not have any variations
                Q(variation__isnull=True)
diff --git a/src/pretix/base/models/orders.py b/src/pretix/base/models/orders.py
index ccf24ef57..b9ff5c503 100644
--- a/src/pretix/base/models/orders.py
+++ b/src/pretix/base/models/orders.py
@@ -5,6 +5,7 @@ from datetime import datetime
 from django.db import models
 from django.utils.timezone import now
 from django.utils.translation import ugettext_lazy as _
+from typing import List, Union
 from versions.models import VersionedForeignKey
 
 from .base import CachedFile, Versionable
@@ -133,7 +134,7 @@ class Order(Versionable):
         verbose_name_plural = _("Orders")
         ordering = ("-datetime",)
 
-    def str(self):
+    def __str__(self):
         return self.full_code
 
     @property
@@ -160,7 +161,7 @@ class Order(Versionable):
                 return
 
     @property
-    def can_modify_answers(self):
+    def can_modify_answers(self) -> bool:
         """
         Is ``True`` if the user can change the question answers / attendee names that are
         related to the order. This checks order status and modification deadlines. It also
@@ -187,7 +188,7 @@ class Order(Versionable):
         order.save()
         return order
 
-    def _can_be_paid(self):
+    def _can_be_paid(self) -> Union[bool, str]:
         error_messages = {
             'late': _("The payment is too late to be accepted."),
         }
@@ -202,7 +203,7 @@ class Order(Versionable):
 
         return self._is_still_available()
 
-    def _is_still_available(self):
+    def _is_still_available(self) -> Union[bool, str]:
         error_messages = {
             'unavailable': _('Some of the ordered products were no longer available.'),
         }
@@ -339,7 +340,7 @@ class OrderPosition(ObjectWithAnswers, Versionable):
         verbose_name_plural = _("Order positions")
 
     @classmethod
-    def transform_cart_positions(cls, cp: list, order) -> list:
+    def transform_cart_positions(cls, cp: List, order) -> list:
         ops = []
         for cartpos in cp:
             op = OrderPosition(
diff --git a/src/pretix/base/models/organizer.py b/src/pretix/base/models/organizer.py
index 61e86a8e3..e038093cb 100644
--- a/src/pretix/base/models/organizer.py
+++ b/src/pretix/base/models/organizer.py
@@ -45,7 +45,7 @@ class Organizer(Versionable):
         verbose_name_plural = _("Organizers")
         ordering = ("name",)
 
-    def __str__(self):
+    def __str__(self) -> str:
         return self.name
 
     def save(self, *args, **kwargs):
@@ -97,7 +97,7 @@ class OrganizerPermission(Versionable):
         verbose_name = _("Organizer permission")
         verbose_name_plural = _("Organizer permissions")
 
-    def __str__(self):
+    def __str__(self) -> str:
         return _("%(name)s on %(object)s") % {
             'name': str(self.user),
             'object': str(self.organizer),
diff --git a/src/pretix/base/payment.py b/src/pretix/base/payment.py
index 9ffcf5468..42af2f0a8 100644
--- a/src/pretix/base/payment.py
+++ b/src/pretix/base/payment.py
@@ -9,8 +9,9 @@ from django.forms import Form
 from django.http import HttpRequest
 from django.template.loader import get_template
 from django.utils.translation import ugettext_lazy as _
+from typing import Any, Dict
 
-from pretix.base.models import CartPosition, Order, Quota
+from pretix.base.models import CartPosition, Event, Order, Quota
 from pretix.base.settings import SettingsSandbox
 from pretix.base.signals import register_payment_providers
 
@@ -20,7 +21,7 @@ class BasePaymentProvider:
     This is the base class for all payment providers.
     """
 
-    def __init__(self, event):
+    def __init__(self, event: Event):
         self.event = event
         self.settings = SettingsSandbox('payment', self.identifier, event)
 
@@ -193,7 +194,7 @@ class BasePaymentProvider:
         """
         raise NotImplementedError()  # NOQA
 
-    def checkout_prepare(self, request: HttpRequest, cart: dict) -> "bool|str":
+    def checkout_prepare(self, request: HttpRequest, cart: Dict[str, Any]) -> "bool|str":
         """
         Will be called after the user selected this provider as his payment method.
         If you provided a form to the user to enter payment data, this method should
@@ -395,7 +396,7 @@ class FreeOrderProvider(BasePaymentProvider):
     def identifier(self) -> str:
         return "free"
 
-    def checkout_confirm_render(self, request) -> str:
+    def checkout_confirm_render(self, request: HttpRequest) -> str:
         return _("No payment is required as this order only includes products which are free of charge.")
 
     def order_pending_render(self, request: HttpRequest, order: Order) -> str:
diff --git a/src/pretix/base/plugins.py b/src/pretix/base/plugins.py
index bba900d38..c01fd9636 100644
--- a/src/pretix/base/plugins.py
+++ b/src/pretix/base/plugins.py
@@ -1,6 +1,7 @@
 from enum import Enum
 
 from django.apps import apps
+from typing import List
 
 
 class PluginType(Enum):
@@ -10,7 +11,7 @@ class PluginType(Enum):
     EXPORT = 4
 
 
-def get_all_plugins() -> "List[class]":
+def get_all_plugins() -> List[type]:
     """
     Returns the PretixPluginMeta classes of all plugins found in the installed Django apps.
     """
diff --git a/src/pretix/base/services/cart.py b/src/pretix/base/services/cart.py
index 400a59185..748d1c96b 100644
--- a/src/pretix/base/services/cart.py
+++ b/src/pretix/base/services/cart.py
@@ -1,9 +1,10 @@
-from datetime import timedelta
+from datetime import datetime, timedelta
 
 from django.conf import settings
 from django.db.models import Q
 from django.utils.timezone import now
 from django.utils.translation import ugettext_lazy as _
+from typing import List, Optional, Tuple
 
 from pretix.base.models import (
     CartPosition, Event, EventLock, Item, ItemVariation, Quota,
@@ -29,7 +30,7 @@ error_messages = {
 }
 
 
-def _extend_existing(event, cart_id, expiry):
+def _extend_existing(event: Event, cart_id: str, expiry: datetime) -> None:
     # Extend this user's cart session to 30 minutes from now to ensure all items in the
     # cart expire at the same time
     # We can extend the reservation of items which are not yet expired without risk
@@ -38,7 +39,7 @@ def _extend_existing(event, cart_id, expiry):
     ).update(expires=expiry)
 
 
-def _re_add_expired_positions(items, event, cart_id):
+def _re_add_expired_positions(items: List[CartPosition], event: Event, cart_id: str) -> List[CartPosition]:
     positions = set()
     # For items that are already expired, we have to delete and re-add them, as they might
     # be no longer available or prices might have changed. Sorry!
@@ -51,20 +52,21 @@ def _re_add_expired_positions(items, event, cart_id):
     return positions
 
 
-def _delete_expired(expired):
+def _delete_expired(expired: List[CartPosition]) -> None:
     for cp in expired:
         if cp.version_end_date is None:
             cp.delete()
 
 
-def _check_date(event):
+def _check_date(event: Event) -> None:
     if event.presale_start and now() < event.presale_start:
         raise CartError(error_messages['not_started'])
     if event.presale_end and now() > event.presale_end:
         raise CartError(error_messages['ended'])
 
 
-def _add_items(event, items, cart_id, expiry):
+def _add_items(event: Event, items: List[Tuple[str, Optional[str], int]],
+               cart_id: str, expiry: datetime) -> Optional[str]:
     err = None
 
     # Fetch items from the database
@@ -129,7 +131,7 @@ def _add_items(event, items, cart_id, expiry):
     return err
 
 
-def _add_items_to_cart(event: Event, items: list, cart_id: str=None):
+def _add_items_to_cart(event: Event, items: List[Tuple[str, Optional[str], int]], cart_id: str=None) -> None:
     with event.lock():
         _check_date(event)
         existing = CartPosition.objects.current.filter(Q(cart_id=cart_id) & Q(event=event)).count()
@@ -150,7 +152,7 @@ def _add_items_to_cart(event: Event, items: list, cart_id: str=None):
             raise CartError(err)
 
 
-def add_items_to_cart(event: str, items: list, cart_id: str=None):
+def add_items_to_cart(event: str, items: List[Tuple[str, Optional[str], int]], cart_id: str=None) -> None:
     """
     Adds a list of items to a user's cart.
     :param event: The event ID in question
@@ -160,12 +162,12 @@ def add_items_to_cart(event: str, items: list, cart_id: str=None):
     """
     event = Event.objects.current.get(identity=event)
     try:
-        return _add_items_to_cart(event, items, cart_id)
+        _add_items_to_cart(event, items, cart_id)
     except EventLock.LockTimeoutException:
         raise CartError(error_messages['busy'])
 
 
-def remove_items_from_cart(event: str, items: list, cart_id: str=None):
+def remove_items_from_cart(event: str, items: List[Tuple[str, Optional[str], int]], cart_id: str=None) -> None:
     """
     Removes a list of items from a user's cart.
     :param event: The event ID in question
@@ -188,10 +190,10 @@ if settings.HAS_CELERY:
     from pretix.celery import app
 
     @app.task(bind=True, max_retries=5, default_retry_delay=2)
-    def add_items_to_cart_task(self, event: str, items: list, cart_id: str):
+    def add_items_to_cart_task(self, event: str, items: List[Tuple[str, Optional[str], int]], cart_id: str):
         event = Event.objects.current.get(identity=event)
         try:
-            return _add_items_to_cart(event, items, cart_id)
+            _add_items_to_cart(event, items, cart_id)
         except EventLock.LockTimeoutException:
             self.retry(exc=CartError(error_messages['busy']))
 
diff --git a/src/pretix/base/services/export.py b/src/pretix/base/services/export.py
index 90807a5cf..cd846c410 100644
--- a/src/pretix/base/services/export.py
+++ b/src/pretix/base/services/export.py
@@ -1,11 +1,12 @@
 from django.conf import settings
 from django.core.files.base import ContentFile
+from typing import Any, Dict
 
 from pretix.base.models import CachedFile, Event, cachedfile_name
 from pretix.base.signals import register_data_exporters
 
 
-def export(event, fileid, provider, form_data):
+def export(event: str, fileid: str, provider: str, form_data: Dict[str, Any]) -> None:
     event = Event.objects.current.get(identity=event)
     file = CachedFile.objects.get(id=fileid)
     responses = register_data_exporters.send(event)
diff --git a/src/pretix/base/services/mail.py b/src/pretix/base/services/mail.py
index a074df708..edd448da2 100644
--- a/src/pretix/base/services/mail.py
+++ b/src/pretix/base/services/mail.py
@@ -5,6 +5,7 @@ from django.core.mail import EmailMessage
 from django.template.loader import get_template
 from django.utils import translation
 from django.utils.translation import ugettext as _
+from typing import Any, Dict
 
 from pretix.base.i18n import LazyI18nString
 from pretix.base.models import Event
@@ -12,7 +13,8 @@ from pretix.base.models import Event
 logger = logging.getLogger('pretix.base.mail')
 
 
-def mail(email: str, subject: str, template: str, context: dict=None, event: Event=None, locale: str=None):
+def mail(email: str, subject: str, template: str,
+         context: Dict[str, Any]=None, event: Event=None, locale: str=None):
     """
     Sends out an email to a user.
 
@@ -58,7 +60,7 @@ def mail(email: str, subject: str, template: str, context: dict=None, event: Eve
         translation.activate(_lng)
 
 
-def mail_send(to, subject, body, sender):
+def mail_send(to: str, subject: str, body: str, sender: str) -> bool:
     email = EmailMessage(subject, body, sender, to=to)
 
     try:
diff --git a/src/pretix/base/services/orders.py b/src/pretix/base/services/orders.py
index 60f6d38eb..557cf62bf 100644
--- a/src/pretix/base/services/orders.py
+++ b/src/pretix/base/services/orders.py
@@ -4,6 +4,7 @@ from django.conf import settings
 from django.db import transaction
 from django.utils.timezone import now
 from django.utils.translation import ugettext_lazy as _
+from typing import List
 
 from pretix.base.models import (
     CartPosition, Event, EventLock, Order, OrderPosition, Quota,
@@ -30,7 +31,7 @@ error_messages = {
 
 
 def mark_order_paid(order: Order, provider: str=None, info: str=None, date: datetime=None, manual: bool=None,
-                    force: bool=False):
+                    force: bool=False) -> Order:
     """
     Marks an order as paid. This clones the order object, sets the payment provider,
     info and date and returns the cloned order object.
@@ -82,14 +83,14 @@ class OrderError(Exception):
     pass
 
 
-def _check_date(event):
+def _check_date(event: Event):
     if event.presale_start and now() < event.presale_start:
         raise OrderError(error_messages['not_started'])
     if event.presale_end and now() > event.presale_end:
         raise OrderError(error_messages['ended'])
 
 
-def _check_positions(event: Event, dt: datetime, positions: list):
+def _check_positions(event: Event, dt: datetime, positions: List[CartPosition]):
     err = None
     _check_date(event)
 
@@ -135,7 +136,7 @@ def _check_positions(event: Event, dt: datetime, positions: list):
 
 
 @transaction.atomic()
-def _create_order(event: Event, email: str, positions: list, dt: datetime,
+def _create_order(event: Event, email: str, positions: List[CartPosition], dt: datetime,
                   payment_provider: BasePaymentProvider, locale: str=None):
     total = sum([c.price for c in positions])
     payment_fee = payment_provider.calculate_fee(total)
@@ -159,7 +160,7 @@ def _create_order(event: Event, email: str, positions: list, dt: datetime,
     return order
 
 
-def _perform_order(event: str, payment_provider: str, position_ids: list,
+def _perform_order(event: str, payment_provider: str, position_ids: List[str],
                    email: str, locale: str):
     event = Event.objects.current.get(identity=event)
     responses = register_payment_providers.send(event)
@@ -197,7 +198,7 @@ def _perform_order(event: str, payment_provider: str, position_ids: list,
         return order.identity
 
 
-def perform_order(event: str, payment_provider: str, positions: list,
+def perform_order(event: str, payment_provider: str, positions: List[str],
                   email: str=None, locale: str=None):
     try:
         return _perform_order(event, payment_provider, positions, email, locale)
@@ -211,7 +212,7 @@ if settings.HAS_CELERY:
     from pretix.celery import app
 
     @app.task(bind=True, max_retries=5, default_retry_delay=2)
-    def perform_order_task(self, event: str, payment_provider: str, positions: list,
+    def perform_order_task(self, event: str, payment_provider: str, positions: List[str],
                            email: str=None, locale: str=None):
         try:
             return _perform_order(event, payment_provider, positions, email, locale)
diff --git a/src/pretix/base/services/stats.py b/src/pretix/base/services/stats.py
index 414449e1f..b91c3d6d0 100644
--- a/src/pretix/base/services/stats.py
+++ b/src/pretix/base/services/stats.py
@@ -1,7 +1,10 @@
+from decimal import Decimal
+
 from django.db.models import Count, Sum
 from django.utils.translation import ugettext_lazy as _
+from typing import Any, Dict, Iterable, List, Tuple
 
-from pretix.base.models import ItemCategory, Order, OrderPosition
+from pretix.base.models import Event, Item, ItemCategory, Order, OrderPosition
 from pretix.base.signals import register_payment_providers
 
 
@@ -10,14 +13,14 @@ class DummyObject:
 
 
 class Dontsum:
-    def __init__(self, value):
+    def __init__(self, value: Any):
         self.value = value
 
-    def __str__(self):
+    def __str__(self) -> str:
         return str(self.value)
 
 
-def tuplesum(tuples):
+def tuplesum(tuples: Iterable[Tuple]) -> Tuple:
     def mysum(it):
         sit = [i for i in it if not isinstance(i, Dontsum)]
         return sum(sit)
@@ -25,7 +28,7 @@ def tuplesum(tuples):
     return tuple(map(mysum, zip(*list(tuples))))
 
 
-def order_overview(event):
+def order_overview(event: Event) -> Tuple[List[Tuple[ItemCategory, List[Item]]], Dict[str, Tuple[Decimal, Decimal]]]:
     items = event.items.all().select_related(
         'category',  # for re-grouping
     ).prefetch_related(
diff --git a/src/pretix/base/services/tickets.py b/src/pretix/base/services/tickets.py
index 3f11e6963..aefd0dbd7 100644
--- a/src/pretix/base/services/tickets.py
+++ b/src/pretix/base/services/tickets.py
@@ -8,7 +8,7 @@ from pretix.base.models import CachedFile, CachedTicket, Order, cachedfile_name
 from pretix.base.signals import register_ticket_outputs
 
 
-def generate(order, provider):
+def generate(order: str, provider: str):
     order = Order.objects.current.select_related('event').get(identity=order)
     ct = CachedTicket.objects.get_or_create(order=order, provider=provider)[0]
     if not ct.cachedfile:
diff --git a/src/pretix/base/settings.py b/src/pretix/base/settings.py
index 26554a90b..a47c46533 100644
--- a/src/pretix/base/settings.py
+++ b/src/pretix/base/settings.py
@@ -7,6 +7,7 @@ from django.conf import settings
 from django.core.files import File
 from django.core.files.storage import default_storage
 from django.db.models import Model
+from typing import Any, Callable, Dict, Optional, TypeVar, Union
 from versions.models import Versionable
 
 DEFAULTS = {
@@ -109,23 +110,23 @@ class SettingsProxy:
     you. It will return None for non-existing properties.
     """
 
-    def __init__(self, obj, parent=None, type=None):
+    def __init__(self, obj: Model, parent: Optional[Model]=None, type=None):
         self._obj = obj
         self._parent = parent
         self._cached_obj = None
         self._type = type
 
-    def _cache(self):
+    def _cache(self) -> Dict[str, Any]:
         if self._cached_obj is None:
             self._cached_obj = {}
             for setting in self._obj.setting_objects.current.all():
                 self._cached_obj[setting.key] = setting
         return self._cached_obj
 
-    def _flush(self):
+    def _flush(self) -> None:
         self._cached_obj = None
 
-    def _unserialize(self, value, as_type):
+    def _unserialize(self, value: str, as_type: type) -> Any:
         if as_type is not None and isinstance(value, as_type):
             return value
         elif value is None:
@@ -155,7 +156,7 @@ class SettingsProxy:
             return as_type.objects.get(pk=value)
         return value
 
-    def _serialize(self, value):
+    def _serialize(self, value: Any) -> str:
         if isinstance(value, str):
             return value
         elif isinstance(value, int) or isinstance(value, float) \
@@ -174,7 +175,7 @@ class SettingsProxy:
 
         raise TypeError('Unable to serialize %s into a setting.' % str(type(value)))
 
-    def get(self, key, default=None, as_type=None):
+    def get(self, key: str, default: Any=None, as_type: type=None):
         """
         Get a setting specified by key 'key'. Normally, settings are strings, but
         if you put non-strings into the settings object, you can request unserialization
@@ -199,21 +200,21 @@ class SettingsProxy:
 
         return self._unserialize(value, as_type)
 
-    def __getitem__(self, key):
+    def __getitem__(self, key: str) -> Any:
         return self.get(key)
 
-    def __getattr__(self, key):
+    def __getattr__(self, key: str) -> Any:
         return self.get(key)
 
-    def __setattr__(self, key, value):
+    def __setattr__(self, key: str, value: Any) -> None:
         if key.startswith('_'):
             return super().__setattr__(key, value)
         self.set(key, value)
 
-    def __setitem__(self, key, value):
+    def __setitem__(self, key: str, value: Any) -> None:
         self.set(key, value)
 
-    def set(self, key, value):
+    def set(self, key: str, value: Any) -> None:
         if key in self._cache():
             s = self._cache()[key]
             s = s.clone()
@@ -223,12 +224,12 @@ class SettingsProxy:
         s.save()
         self._cache()[key] = s
 
-    def __delattr__(self, key):
+    def __delattr__(self, key: str) -> None:
         if key.startswith('_'):
             return super().__delattr__(key)
         return self.__delitem__(key)
 
-    def __delitem__(self, key):
+    def __delitem__(self, key: str) -> None:
         if key in self._cache():
             self._cache()[key].delete()
             del self._cache()[key]
@@ -240,36 +241,36 @@ class SettingsSandbox:
     prefixes for you.
     """
 
-    def __init__(self, type, key, event):
+    def __init__(self, type: str, key: str, event: Versionable):
         self._event = event
         self._type = type
         self._key = key
 
-    def _convert_key(self, key):
+    def _convert_key(self, key: str) -> str:
         return '%s_%s_%s' % (self._type, self._key, key)
 
-    def __setitem__(self, key, value):
+    def __setitem__(self, key: str, value: Any) -> None:
         self.set(key, value)
 
-    def __setattr__(self, key, value):
+    def __setattr__(self, key: str, value: Any) -> None:
         if key.startswith('_'):
             return super().__setattr__(key, value)
         self.set(key, value)
 
-    def __getattr__(self, item):
+    def __getattr__(self, item: str) -> Any:
         return self.get(item)
 
-    def __getitem__(self, item):
+    def __getitem__(self, item: str) -> Any:
         return self.get(item)
 
-    def __delitem__(self, key):
+    def __delitem__(self, key: str) -> None:
         del self._event.settings[self._convert_key(key)]
 
-    def __delattr__(self, key):
+    def __delattr__(self, key: str) -> None:
         del self._event.settings[self._convert_key(key)]
 
-    def get(self, key, default=None, as_type=str):
+    def get(self, key: str, default: Any=None, as_type: type=str):
         return self._event.settings.get(self._convert_key(key), default=default, as_type=as_type)
 
-    def set(self, key, value):
+    def set(self, key: str, value: Any):
         self._event.settings.set(self._convert_key(key), value)
diff --git a/src/pretix/base/signals.py b/src/pretix/base/signals.py
index 2af0e7848..a40fa8707 100644
--- a/src/pretix/base/signals.py
+++ b/src/pretix/base/signals.py
@@ -1,6 +1,7 @@
 import django.dispatch
 from django.apps import apps
 from django.dispatch.dispatcher import NO_RECEIVERS
+from typing import Any, Callable, List, Tuple
 
 from .models import Event
 
@@ -12,7 +13,7 @@ class EventPluginSignal(django.dispatch.Signal):
     Event.
     """
 
-    def send(self, sender, **named):
+    def send(self, sender: Event, **named) -> List[Tuple[Callable, Any]]:
         """
         Send signal from sender to all connected receivers that belong to
         plugins enabled for the given Event.
diff --git a/src/pretix/base/ticketoutput.py b/src/pretix/base/ticketoutput.py
index 53b78b430..7f4deadd5 100644
--- a/src/pretix/base/ticketoutput.py
+++ b/src/pretix/base/ticketoutput.py
@@ -3,8 +3,9 @@ from collections import OrderedDict
 from django import forms
 from django.http import HttpRequest
 from django.utils.translation import ugettext_lazy as _
+from typing import Tuple
 
-from pretix.base.models import Order
+from pretix.base.models import Event, Order
 from pretix.base.settings import SettingsSandbox
 
 
@@ -13,7 +14,7 @@ class BaseTicketOutput:
     This is the base class for all ticket outputs.
     """
 
-    def __init__(self, event):
+    def __init__(self, event: Event):
         self.event = event
         self.settings = SettingsSandbox('ticketoutput', self.identifier, event)
 
@@ -28,7 +29,7 @@ class BaseTicketOutput:
         """
         return self.settings.get('_enabled', as_type=bool)
 
-    def generate(self, order: Order) -> tuple:
+    def generate(self, order: Order) -> Tuple[str, str, str]:
         """
         This method should generate the download file and return a tuple consisting of a
         filename, a file type and file content.
diff --git a/src/pretix/base/types.py b/src/pretix/base/types.py
index 2492efe3f..0913b88c3 100644
--- a/src/pretix/base/types.py
+++ b/src/pretix/base/types.py
@@ -1,3 +1,6 @@
+from typing import Iterable, List, Tuple
+
+
 class VariationDict(dict):
     """
     A VariationDict object behaves exactle the same as the Python built-in
@@ -7,7 +10,7 @@ class VariationDict(dict):
     """
     IGNORE_KEYS = ('variation', 'key', 'available', 'price')
 
-    def relevant_items(self) -> "list[(str, PropertyValue)]":
+    def relevant_items(self) -> Iterable[Tuple]:
         """
         Iterate over all items with numeric keys.
 
@@ -16,7 +19,7 @@ class VariationDict(dict):
         """
         return (i for i in self.items() if i[0] not in self.IGNORE_KEYS)
 
-    def relevant_values(self) -> "list[PropertyValue]":
+    def relevant_values(self) -> Iterable["PropertyValue"]:
         """
         Iterate over all values with numeric keys.
 
@@ -60,14 +63,14 @@ class VariationDict(dict):
         else:
             return super().__eq__(other)
 
-    def empty(self):
+    def empty(self) -> bool:
         """
         Returns true, if this VariationDict does not contain any "real" data like
         references to PropertyValues, but only "metadata".
         """
         return not next(self.relevant_items(), False)
 
-    def ordered_values(self) -> "list[ItemVariation]":
+    def ordered_values(self) -> List["ItemVariation"]:
         """
         Returns a list of values ordered by their keys
         """
@@ -79,7 +82,7 @@ class VariationDict(dict):
             )
         ]
 
-    def __str__(self):
+    def __str__(self) -> str:
         return " – ".join([str(v.value) for v in self.ordered_values()])
 
     def copy(self) -> "VariationDict":
diff --git a/src/pretix/base/views/cachedfiles.py b/src/pretix/base/views/cachedfiles.py
index 31684f786..2f9735646 100644
--- a/src/pretix/base/views/cachedfiles.py
+++ b/src/pretix/base/views/cachedfiles.py
@@ -1,4 +1,4 @@
-from django.http import HttpResponse
+from django.http import HttpRequest, HttpResponse
 from django.shortcuts import get_object_or_404, redirect
 from django.utils.functional import cached_property
 from django.views.generic import TemplateView
@@ -10,10 +10,10 @@ class DownloadView(TemplateView):
     template_name = "pretixbase/cachedfiles/pending.html"
 
     @cached_property
-    def object(self):
+    def object(self) -> CachedFile:
         return get_object_or_404(CachedFile, id=self.kwargs['id'])
 
-    def get(self, request, *args, **kwargs):
+    def get(self, request: HttpRequest, *args, **kwargs) -> HttpResponse:
         if 'ajax' in request.GET:
             return HttpResponse('1' if self.object.file else '0')
         elif self.object.file:
diff --git a/src/requirements/py34.txt b/src/requirements/py34.txt
new file mode 100644
index 000000000..094af98f6
--- /dev/null
+++ b/src/requirements/py34.txt
@@ -0,0 +1,2 @@
+typing
+