diff --git a/.travis.yml b/.travis.yml
index d915fccc..47f53cb0 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -15,16 +15,12 @@ jobs:
       cache: pip
       python: pypy3
 
-    - env: TOXENV=py33
-      python: "3.3"
+    - env: TOXENV=py34
+      python: "3.4"
       after_success: &after_success
         - pip install coveralls
         - coveralls
 
-    - env: TOXENV=py34
-      python: "3.4"
-      after_success: *after_success
-
     - env: TOXENV=py35
       python: "3.5.0"
       after_success: *after_success
@@ -37,6 +33,12 @@ jobs:
       python: "3.6"
       after_success: *after_success
 
+    - env: TOXENV=py37
+      python: "3.7"
+      dist: xenial
+      sudo: required
+      after_success: *after_success
+
     - stage: deploy to pypi
       install: skip
       script: skip
@@ -49,7 +51,7 @@ jobs:
         on:
           tags: true
 
-python: "3.3"
+python: "3.4"
 
 install: pip install tox
 
diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index 3f3ebcb8..460ec105 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -3,6 +3,11 @@ Version history
 
 This library adheres to `Semantic Versioning <http://semver.org/>`_.
 
+**2.2.0**
+
+- Fixed compatibility with Python 3.7
+- Removed support for Python 3.3
+
 **2.1.4** (2018-01-07)
 
 - Removed support for backports.typing, as it has been removed from PyPI
diff --git a/setup.py b/setup.py
index a393e32a..74a46dfb 100644
--- a/setup.py
+++ b/setup.py
@@ -23,20 +23,19 @@
         'License :: OSI Approved :: MIT License',
         'Programming Language :: Python',
         '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'
     ],
     license='MIT',
     zip_safe=True,
     py_modules=['typeguard'],
-    python_requires='>= 3.3',
+    python_requires='>= 3.4',
     setup_requires=[
         'setuptools_scm >= 1.7.0'
     ],
     extras_require={
-        ':python_version == "3.3"': 'typing >= 3.5',
         ':python_version == "3.4"': 'typing >= 3.5',
         'testing': ['pytest', 'pytest-cov']
     }
diff --git a/tox.ini b/tox.ini
index a2e521e0..2b54c9b9 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,6 +1,6 @@
 [tox]
 minversion = 2.5.0
-envlist = pypy3, py33, py34, py35, py36, flake8
+envlist = pypy3, py34, py35, py36, py37, flake8
 skip_missing_interpreters = true
 
 [testenv]
diff --git a/typeguard.py b/typeguard.py
index afc5fa68..b10abdc5 100644
--- a/typeguard.py
+++ b/typeguard.py
@@ -1,4 +1,4 @@
-import collections
+import collections.abc
 import gc
 import inspect
 import sys
@@ -284,6 +284,10 @@ def check_class(argname: str, value, expected_type, memo: _CallMemo) -> None:
         raise TypeError('type of {} must be a type; got {} instead'.format(
             argname, qualified_name(value)))
 
+    # Needed on Python 3.7+
+    if expected_type is Type:
+        return
+
     expected_class = expected_type.__args__[0] if expected_type.__args__ else None
     if expected_class:
         if isinstance(expected_class, TypeVar):
@@ -338,10 +342,19 @@ def check_number(argname: str, value, expected_type):
 
 # Equality checks are applied to these
 origin_type_checkers = {
+    Callable: check_callable,
+    collections.abc.Callable: check_callable,
+    dict: check_dict,
     Dict: check_dict,
+    list: check_list,
     List: check_list,
     Sequence: check_sequence,
+    collections.abc.Sequence: check_sequence,
+    set: check_set,
     Set: check_set,
+    tuple: check_tuple,
+    Tuple: check_tuple,
+    type: check_class,
     Union: check_union
 }
 _subclass_check_unions = hasattr(Union, '__union_set_params__')
@@ -369,18 +382,14 @@ def check_type(argname: str, value, expected_type, memo: _CallMemo) -> None:
         # Only happens on < 3.6
         expected_type = type(None)
 
-    if isclass(expected_type):
-        origin_type = getattr(expected_type, '__origin__', None)
-        if origin_type is not None:
-            checker_func = origin_type_checkers.get(origin_type)
-            if checker_func:
-                checker_func(argname, value, expected_type, memo)
-                return
-
+    origin_type = getattr(expected_type, '__origin__', None)
+    if origin_type is not None:
+        checker_func = origin_type_checkers.get(origin_type)
+        if checker_func:
+            checker_func(argname, value, expected_type, memo)
+    elif isclass(expected_type):
         if issubclass(expected_type, Tuple):
             check_tuple(argname, value, expected_type, memo)
-        elif issubclass(expected_type, Callable) and hasattr(expected_type, '__args__'):
-            check_callable(argname, value, expected_type, memo)
         elif issubclass(expected_type, (float, complex)):
             check_number(argname, value, expected_type)
         elif _subclass_check_unions and issubclass(expected_type, Union):
@@ -397,9 +406,6 @@ def check_type(argname: str, value, expected_type, memo: _CallMemo) -> None:
     elif isinstance(expected_type, TypeVar):
         # Only happens on < 3.6
         check_typevar(argname, value, expected_type, memo)
-    elif getattr(expected_type, '__origin__', None) is Union:
-        # Only happens on 3.6+
-        check_union(argname, value, expected_type, memo)
 
 
 def check_return_type(retval, memo: _CallMemo) -> bool: