diff --git a/.travis.yml b/.travis.yml
index d46a30738..a712a664d 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -2,7 +2,6 @@ language: python
 dist: xenial
 python:
   - 2.7
-  - 3.4
   - 3.5
   - 3.6
   - 3.7
diff --git a/CHANGES.rst b/CHANGES.rst
index 4d2f513a8..a8968eb96 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -2,14 +2,17 @@
  Change History
 ================
 
-5.5.2 (unreleased)
+5.6.0 (unreleased)
 ==================
 
 - Make repozo's recover mode atomic by recovering the backup in a
   temporary file which is then moved to the expected output file.
+
 - Add a new option to repozo in recover mode which allows to verify
   backups integrity on the fly.
 
+- Drop support for Python 3.4.
+
 5.5.1 (2018-10-25)
 ==================
 
diff --git a/appveyor.yml b/appveyor.yml
index 6db27534b..ddbf0e045 100644
--- a/appveyor.yml
+++ b/appveyor.yml
@@ -2,8 +2,6 @@ environment:
   matrix:
     - python: 27
     - python: 27-x64
-    - python: 34
-    - python: 34-x64
     - python: 35
     - python: 35-x64
     - python: 36
diff --git a/setup.py b/setup.py
index bb47c4d1d..331adbcdc 100644
--- a/setup.py
+++ b/setup.py
@@ -13,7 +13,7 @@
 ##############################################################################
 from setuptools import setup, find_packages
 
-version = '5.5.2.dev0'
+version = '5.6.0.dev0'
 
 classifiers = """\
 Intended Audience :: Developers
@@ -22,7 +22,6 @@
 Programming Language :: Python :: 2
 Programming Language :: Python :: 2.7
 Programming Language :: Python :: 3
-Programming Language :: Python :: 3.4
 Programming Language :: Python :: 3.5
 Programming Language :: Python :: 3.6
 Programming Language :: Python :: 3.7
@@ -88,5 +87,5 @@ def read(path):
       repozo = ZODB.scripts.repozo:main
     """,
     include_package_data=True,
-    python_requires='>=2.7,!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*',
+    python_requires='>=2.7,!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,!=3.4.*',
 )
diff --git a/tox.ini b/tox.ini
index 5546f69b2..357af3695 100644
--- a/tox.ini
+++ b/tox.ini
@@ -2,7 +2,7 @@
 # Jython 2.7rc2 does work, but unfortunately has an issue running
 # with Tox 1.9.2 (http://bugs.jython.org/issue2325)
 #envlist = py26,py27,py33,py34,pypy,simple,jython,pypy3
-envlist = py27,py34,py35,py36,py37,pypy,pypy3
+envlist = py27,py35,py36,py37,pypy,pypy3
 
 [testenv]
 # ZODB.tests.testdocumentation needs to find