diff --git a/build-requirements.txt b/build-requirements.txt
index eee2f9da3fe3..aad1f8e59105 100644
--- a/build-requirements.txt
+++ b/build-requirements.txt
@@ -1,4 +1,3 @@
 -r mypy-requirements.txt
 types-typed-ast>=1.4.0,<1.5.0
 types-toml>=0.0
-types-enum34>=0.0; python_version == '3.5'
diff --git a/docs/source/class_basics.rst b/docs/source/class_basics.rst
index 330d9805be14..8e604427e683 100644
--- a/docs/source/class_basics.rst
+++ b/docs/source/class_basics.rst
@@ -127,12 +127,6 @@ particular attribute should not be set on instances:
   a.x = 1  # Error: Cannot assign to class variable "x" via instance
   print(a.x)  # OK -- can be read through an instance
 
-.. note::
-
-   If you need to support Python 3 versions 3.5.2 or earlier, you have
-   to import ``ClassVar`` from ``typing_extensions`` instead (available on
-   PyPI). If you use Python 2.7, you can import it from ``typing``.
-
 It's not necessary to annotate all class variables using
 :py:data:`~typing.ClassVar`. An attribute without the :py:data:`~typing.ClassVar` annotation can
 still be used as a class variable. However, mypy won't prevent it from
diff --git a/docs/source/common_issues.rst b/docs/source/common_issues.rst
index 0a513efc2d4f..58f8395091d0 100644
--- a/docs/source/common_issues.rst
+++ b/docs/source/common_issues.rst
@@ -14,7 +14,7 @@ Can't install mypy using pip
 
 If installation fails, you've probably hit one of these issues:
 
-* Mypy needs Python 3.5 or later to run.
+* Mypy needs Python 3.6 or later to run.
 * You may have to run pip like this:
   ``python3 -m pip install mypy``.
 
@@ -428,8 +428,8 @@ More specifically, mypy will understand the use of :py:data:`sys.version_info` a
    import sys
 
    # Distinguishing between different versions of Python:
-   if sys.version_info >= (3, 5):
-       # Python 3.5+ specific definitions and imports
+   if sys.version_info >= (3, 8):
+       # Python 3.8+ specific definitions and imports
    elif sys.version_info[0] >= 3:
        # Python 3 specific definitions and imports
    else:
diff --git a/docs/source/getting_started.rst b/docs/source/getting_started.rst
index 12c05c0d32e0..d180fcd70f3c 100644
--- a/docs/source/getting_started.rst
+++ b/docs/source/getting_started.rst
@@ -12,7 +12,7 @@ may not make much sense otherwise.
 Installing and running mypy
 ***************************
 
-Mypy requires Python 3.5 or later to run.  Once you've
+Mypy requires Python 3.6 or later to run.  Once you've
 `installed Python 3 <https://www.python.org/downloads/>`_,
 install mypy using pip:
 
diff --git a/docs/source/runtime_troubles.rst b/docs/source/runtime_troubles.rst
index 34d9dc795f0d..515a7985dcbe 100644
--- a/docs/source/runtime_troubles.rst
+++ b/docs/source/runtime_troubles.rst
@@ -94,12 +94,6 @@ Since code inside ``if TYPE_CHECKING:`` is not executed at runtime, it provides
 a convenient way to tell mypy something without the code being evaluated at
 runtime. This is most useful for resolving :ref:`import cycles <import-cycles>`.
 
-.. note::
-
-   Python 3.5.1 and below don't have :py:data:`~typing.TYPE_CHECKING`. An
-   alternative is to define a constant named ``MYPY`` that has the value
-   ``False`` at runtime. Mypy considers it to be ``True`` when type checking.
-
 Class name forward references
 -----------------------------
 
diff --git a/mypy/build.py b/mypy/build.py
index a39b78798d98..14bf1e68a51e 100644
--- a/mypy/build.py
+++ b/mypy/build.py
@@ -1091,7 +1091,7 @@ def _load_json_file(file: str, manager: BuildManager,
         manager.trace(log_success + data.rstrip())
     try:
         result = json.loads(data)
-    except ValueError:  # TODO: JSONDecodeError in 3.5
+    except json.JSONDecodeError:
         manager.errors.set_file(file, None)
         manager.errors.report(-1, -1,
                               "Error reading JSON file;"
diff --git a/mypy/fastparse.py b/mypy/fastparse.py
index 15b86d71b3d2..ed85c5962424 100644
--- a/mypy/fastparse.py
+++ b/mypy/fastparse.py
@@ -1357,7 +1357,7 @@ def translate_expr_list(self, l: Sequence[ast3.expr]) -> List[Type]:
 
     def visit_raw_str(self, s: str) -> Type:
         # An escape hatch that allows the AST walker in fastparse2 to
-        # directly hook into the Python 3.5 type converter in some cases
+        # directly hook into the Python 3 type converter in some cases
         # without needing to create an intermediary `Str` object.
         _, typ = parse_type_comment(s.strip(),
                                     self.line,
diff --git a/mypy/main.py b/mypy/main.py
index da4eda6e04a0..ac71d035c75b 100644
--- a/mypy/main.py
+++ b/mypy/main.py
@@ -237,8 +237,8 @@ class PythonExecutableInferenceError(Exception):
 def python_executable_prefix(v: str) -> List[str]:
     if sys.platform == 'win32':
         # on Windows, all Python executables are named `python`. To handle this, there
-        # is the `py` launcher, which can be passed a version e.g. `py -3.5`, and it will
-        # execute an installed Python 3.5 interpreter. See also:
+        # is the `py` launcher, which can be passed a version e.g. `py -3.8`, and it will
+        # execute an installed Python 3.8 interpreter. See also:
         # https://docs.python.org/3/using/windows.html#python-launcher-for-windows
         return ['py', '-{}'.format(v)]
     else:
diff --git a/mypy/stubtest.py b/mypy/stubtest.py
index 7915e14f1551..2dde3e7f931e 100644
--- a/mypy/stubtest.py
+++ b/mypy/stubtest.py
@@ -38,17 +38,7 @@ def __repr__(self) -> str:
 MISSING = Missing()
 
 T = TypeVar("T")
-if sys.version_info >= (3, 5, 3):
-    MaybeMissing = Union[T, Missing]
-else:
-    # work around a bug in 3.5.2 and earlier's typing.py
-    class MaybeMissingMeta(type):
-        def __getitem__(self, arg: Any) -> Any:
-            return Union[arg, Missing]
-
-    class MaybeMissing(metaclass=MaybeMissingMeta):  # type: ignore
-        pass
-
+MaybeMissing = Union[T, Missing]
 
 _formatter = FancyFormatter(sys.stdout, sys.stderr, False)
 
@@ -1069,7 +1059,7 @@ def get_typeshed_stdlib_modules(custom_typeshed_dir: Optional[str]) -> List[str]
     """Returns a list of stdlib modules in typeshed (for current Python version)."""
     stdlib_py_versions = mypy.modulefinder.load_stdlib_py_versions(custom_typeshed_dir)
     packages = set()
-    # Typeshed doesn't cover Python 3.5.
+    # Typeshed's minimum supported Python 3 is Python 3.6
     if sys.version_info < (3, 6):
         version_info = (3, 6)
     else:
diff --git a/mypy/util.py b/mypy/util.py
index 79475972a57a..2c1ffbce43cf 100644
--- a/mypy/util.py
+++ b/mypy/util.py
@@ -393,13 +393,9 @@ def get_unique_redefinition_name(name: str, existing: Container[str]) -> str:
 def check_python_version(program: str) -> None:
     """Report issues with the Python used to run mypy, dmypy, or stubgen"""
     # Check for known bad Python versions.
-    if sys.version_info[:2] < (3, 5):
-        sys.exit("Running {name} with Python 3.4 or lower is not supported; "
-                 "please upgrade to 3.5 or newer".format(name=program))
-    # this can be deleted once we drop support for 3.5
-    if sys.version_info[:3] == (3, 5, 0):
-        sys.exit("Running {name} with Python 3.5.0 is not supported; "
-                 "please upgrade to 3.5.1 or newer".format(name=program))
+    if sys.version_info[:2] < (3, 6):
+        sys.exit("Running {name} with Python 3.5 or lower is not supported; "
+                 "please upgrade to 3.6 or newer".format(name=program))
 
 
 def count_stats(errors: List[str]) -> Tuple[int, int]:
diff --git a/setup.py b/setup.py
index 87e5b8432d34..ca3a7ebbace1 100644
--- a/setup.py
+++ b/setup.py
@@ -5,8 +5,8 @@
 import os.path
 import sys
 
-if sys.version_info < (3, 5, 0):
-    sys.stderr.write("ERROR: You need Python 3.5 or later to use mypy.\n")
+if sys.version_info < (3, 6, 0):
+    sys.stderr.write("ERROR: You need Python 3.6 or later to use mypy.\n")
     exit(1)
 
 # we'll import stuff from the source tree, let's ensure is on the sys path
@@ -162,7 +162,6 @@ def run(self):
     'Intended Audience :: Developers',
     'License :: OSI Approved :: MIT License',
     'Programming Language :: Python :: 3',
-    'Programming Language :: Python :: 3.5',
     'Programming Language :: Python :: 3.6',
     'Programming Language :: Python :: 3.7',
     'Programming Language :: Python :: 3.8',
@@ -198,7 +197,7 @@ def run(self):
                         ],
       # Same here.
       extras_require={'dmypy': 'psutil >= 4.0', 'python2': 'typed_ast >= 1.4.0, < 1.5.0'},
-      python_requires=">=3.5",
+      python_requires=">=3.6",
       include_package_data=True,
       project_urls={
           'News': 'http://mypy-lang.org/news.html',
diff --git a/test-requirements.txt b/test-requirements.txt
index 2d83221c2f7a..b5b9da8b0a24 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -6,8 +6,7 @@ flake8-bugbear; python_version >= '3.5'
 flake8-pyi>=20.5; python_version >= '3.6'
 lxml>=4.4.0
 psutil>=4.0
-# pytest 6.2 does not support Python 3.5
-pytest>=6.1.0,<6.2.0
+pytest>=6.2.0,<7.0.0
 pytest-xdist>=1.34.0,<2.0.0
 pytest-forked>=1.3.0,<2.0.0
 pytest-cov>=2.10.0,<3.0.0