diff --git a/.travis.yml b/.travis.yml
index 98897ef..3e75c1c 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,13 +1,24 @@
 language: python
 python:
     - 2.7
-    - 3.3
     - 3.4
     - 3.5
+    - 3.6
     - pypy
+    - pypy3
+matrix:
+    include:
+        - python: "3.7"
+          dist: xenial
+before_install:
+    - pip install -U pip setuptools
+    - pip install -U coverage coveralls
 install:
-    - pip install tox-travis
+    - pip install -U -e .[test]
 script:
-    - tox
+    - coverage run -m zope.testrunner --test-path=src
+after_success:
+    - coveralls
 notifications:
     email: false
+cache: pip
diff --git a/CHANGES.txt b/CHANGES.txt
index 10f2eaa..f004882 100644
--- a/CHANGES.txt
+++ b/CHANGES.txt
@@ -4,7 +4,9 @@ Changelog
 4.1.0 (unreleased)
 ------------------
 
-- Nothing changed yet.
+- Add support for Python 3.6, 3.7 and PyPy3.
+
+- Drop support for Python 3.3.
 
 
 4.0.0 (2016-08-08)
diff --git a/setup.py b/setup.py
index c30171c..13e88ac 100644
--- a/setup.py
+++ b/setup.py
@@ -55,9 +55,10 @@ def read(*rnames):
         'Programming Language :: Python :: 2',
         'Programming Language :: Python :: 2.7',
         'Programming Language :: Python :: 3',
-        'Programming Language :: Python :: 3.3',
         'Programming Language :: Python :: 3.4',
         'Programming Language :: Python :: 3.5',
+        'Programming Language :: Python :: 3.6',
+        'Programming Language :: Python :: 3.7',
         'Programming Language :: Python :: Implementation',
         'Programming Language :: Python :: Implementation :: CPython',
         'Programming Language :: Python :: Implementation :: PyPy',
@@ -65,7 +66,7 @@ def read(*rnames):
         'Operating System :: OS Independent',
         'Topic :: Internet :: WWW/HTTP',
         'Framework :: Zope :: 3'],
-    url='http://pypi.python.org/pypi/zope.app.appsetup',
+    url='https://github.com/zopefoundation/zope.app.appsetup',
     packages=find_packages('src'),
     package_dir={'': 'src'},
     namespace_packages=['zope', 'zope.app'],
diff --git a/src/zope/app/appsetup/bootstrap.py b/src/zope/app/appsetup/bootstrap.py
index 0a8b393..4893218 100644
--- a/src/zope/app/appsetup/bootstrap.py
+++ b/src/zope/app/appsetup/bootstrap.py
@@ -180,7 +180,7 @@ def checkSecurityPolicy(event):
     was refactored and now it needs to be included from site.zcml.
     """
     if getSecurityPolicy() is ParanoidSecurityPolicy:
-        logging.getLogger('zope.app.appsetup').warn(
+        logging.getLogger('zope.app.appsetup').warning(
             'Security policy is not configured.\n'
             'Please make sure that securitypolicy.zcml is included'
             ' in site.zcml immediately\n'
diff --git a/src/zope/app/appsetup/bootstrap.txt b/src/zope/app/appsetup/bootstrap.txt
index 365e47a..3fe51a8 100644
--- a/src/zope/app/appsetup/bootstrap.txt
+++ b/src/zope/app/appsetup/bootstrap.txt
@@ -10,8 +10,8 @@ object.  It subscribes to DatabaseOpened events:
     >>> from zope.app.appsetup import bootstrap
     >>> import zope.processlifetime
 
-    >>> from ZODB.tests import util
-    >>> db = util.DB()
+    >>> from ZODB.MappingStorage import DB
+    >>> db = DB()
     >>> bootstrap.bootStrapSubscriber(zope.processlifetime.DatabaseOpened(db))
 
 The subscriber makes sure that there is a root folder:
diff --git a/src/zope/app/appsetup/debug.py b/src/zope/app/appsetup/debug.py
index 9e19f4a..db9431b 100644
--- a/src/zope/app/appsetup/debug.py
+++ b/src/zope/app/appsetup/debug.py
@@ -60,7 +60,8 @@ def main(args=None):
     db = loadApplication(args)
     if "PYTHONSTARTUP" in os.environ:
         startup = os.environ["PYTHONSTARTUP"]
-        exec(compile(open(startup).read(), startup, 'exec'))
+        with open(startup) as s:
+            exec(compile(s.read(), startup, 'exec'))
     sys.modules['__main__'].root = db.open().root()[ZopePublication.root_name]
     print('The application root is known as `root`.')
     os.environ["PYTHONINSPECT"] = "true"
diff --git a/src/zope/app/appsetup/tests.py b/src/zope/app/appsetup/tests.py
index e9a4444..cc81201 100644
--- a/src/zope/app/appsetup/tests.py
+++ b/src/zope/app/appsetup/tests.py
@@ -27,7 +27,7 @@
 
 import zope.component
 
-from ZODB.tests.util import DB
+from ZODB.MappingStorage import DB
 from zope.traversing.api import traverse, getPath
 from zope.error.interfaces import IErrorReportingUtility
 from zope.error.error import ErrorReportingUtility
diff --git a/tox.ini b/tox.ini
index 1667049..b92260a 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,29 +1,22 @@
 [tox]
-envlist = coverage-clean, py27, py33, py34, py35, pypy, coverage-report
+envlist = flake8, py27, py34, py35, py36, py37, pypy, pypy3, coverage
 
 [testenv]
+usedevelop = true
 commands =
-    coverage run setup.py ftest
-setenv =
-  COVERAGE_FILE=.coverage.{envname}
+    zope-testrunner --test-path=src []
+extras = test
+
+[testenv:coverage]
+basepython = python3.7
+commands =
+    coverage run -m zope.testrunner --test-path=src []
+    coverage report --fail-under=80
 deps =
-    .[test]
     coverage
 
-[testenv:coverage-clean]
-deps = coverage
-setenv =
-  COVERAGE_FILE=.coverage
+[testenv:flake8]
+basepython = python3.6
 skip_install = true
-commands = coverage erase
-
-[testenv:coverage-report]
-deps = coverage
-setenv =
-  COVERAGE_FILE=.coverage
-skip_install = true
-commands =
-    coverage combine
-    coverage report
-    coverage html
-    coverage xml
+deps = flake8
+commands = flake8 --doctests src setup.py