diff --git a/.travis.yml b/.travis.yml
index 92644b282..6819d8ae9 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,14 +1,13 @@
 language: python
 python:
-  - "pypy2.7-5.10.0"
   - "2.7"
-  - "3.5"
   - "3.6"
   - "3.7"
+  - "3.8"
 install:
   - pip install --upgrade setuptools tox tox-travis coveralls
 dist:
-  - xenial
+  - bionic
 script:
   - tox
 after_success:
diff --git a/README.rst b/README.rst
index 4e378ef88..2de09c158 100644
--- a/README.rst
+++ b/README.rst
@@ -99,7 +99,7 @@ How to Use
 Prerequisites
 -------------
 
-Python 2.7 or Python 3.5+
+Python 2.7 or Python 3.6+
 
 Installing It
 -------------
diff --git a/setup.py b/setup.py
index daeae8e23..bd8bfb0c4 100755
--- a/setup.py
+++ b/setup.py
@@ -118,9 +118,9 @@ def readme():
     classifiers=[
         'Programming Language :: Python',
         'Programming Language :: Python :: 2.7',
-        'Programming Language :: Python :: 3.5',
         'Programming Language :: Python :: 3.6',
         'Programming Language :: Python :: 3.7',
+        'Programming Language :: Python :: 3.8',
         'Development Status :: 5 - Production/Stable',
         'Intended Audience :: Developers',
         'Operating System :: OS Independent',
diff --git a/tox.ini b/tox.ini
index e814f8508..bc1bee26f 100644
--- a/tox.ini
+++ b/tox.ini
@@ -4,22 +4,20 @@ exclude=connexion/__init__.py
 
 [tox]
 envlist =
-    {pypy}-{min,pypi,dev}
     {py27}-{min,pypi,dev}
-    {py35}-{min,pypi,dev}
     {py36}-{min,pypi,dev}
     {py37}-{min,pypi,dev}
+    {py38}-{min,pypi,dev}
     isort-check
     isort-check-examples
     isort-check-tests
     flake8
 
 [travis]
-pypy=pypy-min,pypy-pypi
 2.7=py27-min,py27-pypi
-3.5=py35-min,py35-pypi
 3.6=py36-min,py36-pypi
 3.7=py37-min,py37-pypi,isort-check,isort-check-examples,isort-check-tests,flake8
+3.8=py38-min
 
 [testenv]
 setenv=PYTHONPATH = {toxinidir}:{toxinidir}
@@ -32,7 +30,7 @@ commands=
     pypi: pip install -r {toxworkdir}/requirements-pypi.txt
     dev: requirements-builder --level=dev --req=requirements-devel.txt -o {toxworkdir}/requirements-dev.txt setup.py
     dev: pip install -r {toxworkdir}/requirements-dev.txt
-    py3{5,6,7}: pip install -r requirements-aiohttp.txt
+    py3{6,7,8}: pip install -r requirements-aiohttp.txt
     python setup.py test
 
 [testenv:flake8]