diff --git a/.travis.yml b/.travis.yml
index e01b83f41..82184c5bf 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,4 +1,5 @@
 language: python
+dist: xenial
 sudo: false
 install:
   - pip install -U pip wheel setuptools
@@ -12,23 +13,23 @@ services:
   - postgresql
 matrix:
   include:
-    - python: 3.6
+    - python: 3.7
       env: JOB=tests PRETIX_CONFIG_FILE=tests/travis_sqlite.cfg
-    - python: 3.6
+    - python: 3.7
       env: JOB=tests-cov PRETIX_CONFIG_FILE=tests/travis_postgres.cfg
-    - python: 3.6
+    - python: 3.7
       env: JOB=style
-    - python: 3.6
+    - python: 3.7
       env: JOB=tests PRETIX_CONFIG_FILE=tests/travis_mysql.cfg
-    - python: 3.6
+    - python: 3.7
       env: JOB=tests PRETIX_CONFIG_FILE=tests/travis_postgres.cfg
     - python: 3.5
       env: JOB=tests PRETIX_CONFIG_FILE=tests/travis_postgres.cfg
-    - python: 3.6
+    - python: 3.7
       env: JOB=plugins
-    - python: 3.6
+    - python: 3.7
       env: JOB=doc-spelling
-    - python: 3.6
+    - python: 3.7
       env: JOB=translation-spelling
 addons:
   postgresql: "9.4"
diff --git a/doc/admin/installation/manual_smallscale.rst b/doc/admin/installation/manual_smallscale.rst
index a5110c50f..aeff2c66b 100644
--- a/doc/admin/installation/manual_smallscale.rst
+++ b/doc/admin/installation/manual_smallscale.rst
@@ -68,10 +68,6 @@ To build and run pretix, you will need the following debian packages::
                       python3-dev libxml2-dev libxslt1-dev libffi-dev zlib1g-dev libssl-dev \
                       gettext libpq-dev libmariadbclient-dev libjpeg-dev libopenjp2-7-dev
 
-.. note:: Python 3.7 is not yet supported, so if you run a very recent OS, make sure to get
-          Python 3.6 from somewhere. You can check the current state of things in our
-          `Python 3.7 issue`_.
-
 Config file
 -----------
 
@@ -314,4 +310,3 @@ example::
 .. _redis: https://blog.programster.org/debian-8-install-redis-server/
 .. _ufw: https://en.wikipedia.org/wiki/Uncomplicated_Firewall
 .. _strong encryption settings: https://mozilla.github.io/server-side-tls/ssl-config-generator/
-.. _Python 3.7 issue: https://github.com/pretix/pretix/issues/1025
diff --git a/src/requirements/production.txt b/src/requirements/production.txt
index a5fbb7ffa..2f109447e 100644
--- a/src/requirements/production.txt
+++ b/src/requirements/production.txt
@@ -16,8 +16,8 @@ libsass
 django-otp==0.4.*
 python-u2flib-server==4.*
 django-formtools==2.1
-celery>=4.1.1,<4.2.0
-kombu==4.2.*
+celery==4.3.*
+kombu==4.5.*
 django-statici18n==1.8.*
 inlinestyler==0.2.*
 BeautifulSoup4==4.7.*
@@ -54,5 +54,5 @@ defusedcsv>=1.0.1
 vat_moss==0.11.0
 django-localflavor
 idna==2.6 # required by current requests
-django-redis==4.8.*
-redis==2.10.5
+django-redis==4.10.*
+redis==3.2.*
diff --git a/src/setup.py b/src/setup.py
index 914a3f3a8..db1a09616 100644
--- a/src/setup.py
+++ b/src/setup.py
@@ -104,8 +104,8 @@ setup(
         'django-otp==0.4.*',
         'python-u2flib-server==4.*',
         'django-formtools==2.1',
-        'celery>=4.1.1,<4.2.0',
-        'kombu==4.2.*',
+        'celery==4.3.*',
+        'kombu==4.5.*',
         'django-statici18n==1.8.*',
         'inlinestyler==0.2.*',
         'BeautifulSoup4==4.7.*',
@@ -121,8 +121,8 @@ setup(
         'babel',
         'paypalrestsdk==1.13.*',
         'pycparser==2.13',
-        'django-redis==4.8.*',
-        'redis==2.10.5',
+        'django-redis==4.10.*',
+        'redis==3.2.*',
         'stripe==2.0.*',
         'chardet<3.1.0,>=3.0.2',
         'mt-940==3.2',