diff --git a/src/pip/_internal/pep425tags.py b/src/pip/_internal/pep425tags.py
index 07dc148eec3..03a906b94bc 100644
--- a/src/pip/_internal/pep425tags.py
+++ b/src/pip/_internal/pep425tags.py
@@ -16,7 +16,7 @@
 
 if MYPY_CHECK_RUNNING:
     from typing import (
-        Tuple, Callable, List, Optional, Union, Dict
+        Tuple, Callable, List, Optional, Union, Dict, Set
     )
 
     Pep425Tag = Tuple[str, str, str]
@@ -105,6 +105,8 @@ def get_abi_tag():
     (CPython 2, PyPy)."""
     soabi = get_config_var('SOABI')
     impl = get_abbr_impl()
+    abi = None  # type: Optional[str]
+
     if not soabi and impl in {'cp', 'pp'} and hasattr(sys, 'maxunicode'):
         d = ''
         m = ''
@@ -129,8 +131,7 @@ def get_abi_tag():
         abi = 'cp' + soabi.split('-')[1]
     elif soabi:
         abi = soabi.replace('.', '_').replace('-', '_')
-    else:
-        abi = None
+
     return abi
 
 
@@ -310,7 +311,7 @@ def get_supported(
     if abi:
         abis[0:0] = [abi]
 
-    abi3s = set()
+    abi3s = set()  # type: Set[str]
     for suffix in get_extension_suffixes():
         if suffix.startswith('.abi'):
             abi3s.add(suffix.split('.', 2)[1])
diff --git a/src/pip/_internal/utils/appdirs.py b/src/pip/_internal/utils/appdirs.py
index fb2611104c8..dcd757c7e05 100644
--- a/src/pip/_internal/utils/appdirs.py
+++ b/src/pip/_internal/utils/appdirs.py
@@ -218,6 +218,8 @@ def _get_win_folder_from_registry(csidl_name):
 
 def _get_win_folder_with_ctypes(csidl_name):
     # type: (str) -> str
+    # On Python 2, ctypes.create_unicode_buffer().value returns "unicode",
+    # which isn't the same as str in the annotation above.
     csidl_const = {
         "CSIDL_APPDATA": 26,
         "CSIDL_COMMON_APPDATA": 35,
@@ -239,7 +241,8 @@ def _get_win_folder_with_ctypes(csidl_name):
         if ctypes.windll.kernel32.GetShortPathNameW(buf.value, buf2, 1024):
             buf = buf2
 
-    return buf.value
+    # The type: ignore is explained under the type annotation for this function
+    return buf.value  # type: ignore
 
 
 if WINDOWS:
diff --git a/src/pip/_internal/utils/misc.py b/src/pip/_internal/utils/misc.py
index f094cac990d..a08669a4b85 100644
--- a/src/pip/_internal/utils/misc.py
+++ b/src/pip/_internal/utils/misc.py
@@ -53,21 +53,18 @@
 if MYPY_CHECK_RUNNING:
     from typing import (
         Any, AnyStr, Container, Iterable, List, Mapping, Match, Optional, Text,
-        Union,
+        Tuple, Union, cast,
     )
     from pip._vendor.pkg_resources import Distribution
     from pip._internal.models.link import Link
     from pip._internal.utils.ui import SpinnerInterface
 
-try:
-    from typing import cast, Tuple
     VersionInfo = Tuple[int, int, int]
-except ImportError:
-    # typing's cast() isn't supported in code comments, so we need to
-    # define a dummy, no-op version.
-    def cast(typ, val):
-        return val
-    VersionInfo = None
+else:
+    # typing's cast() is needed at runtime, but we don't want to import typing.
+    # Thus, we use a dummy no-op version, which we tell mypy to ignore.
+    def cast(type_, value):  # type: ignore
+        return value
 
 
 __all__ = ['rmtree', 'display_path', 'backup_dir',
@@ -140,7 +137,7 @@ def normalize_version_info(py_version_info):
     elif len(py_version_info) > 3:
         py_version_info = py_version_info[:3]
 
-    return cast(VersionInfo, py_version_info)
+    return cast('VersionInfo', py_version_info)
 
 
 def ensure_dir(path):
diff --git a/tools/mypy-requirements.txt b/tools/mypy-requirements.txt
index ac69c5ad480..50615d913be 100644
--- a/tools/mypy-requirements.txt
+++ b/tools/mypy-requirements.txt
@@ -1 +1 @@
-mypy == 0.670
+mypy == 0.720