diff --git a/src/_pytest/assertion/rewrite.py b/src/_pytest/assertion/rewrite.py
index c225eff5f..4e7db8369 100644
--- a/src/_pytest/assertion/rewrite.py
+++ b/src/_pytest/assertion/rewrite.py
@@ -78,7 +78,8 @@ class AssertionRewritingHook(importlib.abc.MetaPathFinder):
             # there's nothing to rewrite there
             # python3.5 - python3.6: `namespace`
             # python3.7+: `None`
-            or spec.origin in {None, "namespace"}
+            or spec.origin == "namespace"
+            or spec.origin is None
             # we can only rewrite source files
             or not isinstance(spec.loader, importlib.machinery.SourceFileLoader)
             # if the file doesn't exist, we can't rewrite it
@@ -743,8 +744,7 @@ class AssertionRewriter(ast.NodeVisitor):
             from _pytest.warning_types import PytestAssertRewriteWarning
             import warnings
 
-            # Ignore type: typeshed bug https://github.com/python/typeshed/pull/3121
-            warnings.warn_explicit(  # type: ignore
+            warnings.warn_explicit(
                 PytestAssertRewriteWarning(
                     "assertion is always true, perhaps remove parentheses?"
                 ),
diff --git a/src/_pytest/cacheprovider.py b/src/_pytest/cacheprovider.py
index 7a5deaa39..dad76f13f 100755
--- a/src/_pytest/cacheprovider.py
+++ b/src/_pytest/cacheprovider.py
@@ -7,6 +7,7 @@ ignores the external pytest-cache
 import json
 import os
 from collections import OrderedDict
+from typing import List
 
 import attr
 import py
@@ -15,6 +16,9 @@ import pytest
 from .pathlib import Path
 from .pathlib import resolve_from_str
 from .pathlib import rm_rf
+from _pytest import nodes
+from _pytest.config import Config
+from _pytest.main import Session
 
 README_CONTENT = """\
 # pytest cache directory #
@@ -263,10 +267,12 @@ class NFPlugin:
         self.active = config.option.newfirst
         self.cached_nodeids = config.cache.get("cache/nodeids", [])
 
-    def pytest_collection_modifyitems(self, session, config, items):
+    def pytest_collection_modifyitems(
+        self, session: Session, config: Config, items: List[nodes.Item]
+    ) -> None:
         if self.active:
-            new_items = OrderedDict()
-            other_items = OrderedDict()
+            new_items = OrderedDict()  # type: OrderedDict[str, nodes.Item]
+            other_items = OrderedDict()  # type: OrderedDict[str, nodes.Item]
             for item in items:
                 if item.nodeid not in self.cached_nodeids:
                     new_items[item.nodeid] = item
diff --git a/src/_pytest/capture.py b/src/_pytest/capture.py
index c4099e6b0..56707822d 100644
--- a/src/_pytest/capture.py
+++ b/src/_pytest/capture.py
@@ -12,6 +12,7 @@ from tempfile import TemporaryFile
 
 import pytest
 from _pytest.compat import CaptureIO
+from _pytest.fixtures import FixtureRequest
 
 patchsysdict = {0: "stdin", 1: "stdout", 2: "stderr"}
 
@@ -241,13 +242,12 @@ class CaptureManager:
 capture_fixtures = {"capfd", "capfdbinary", "capsys", "capsysbinary"}
 
 
-def _ensure_only_one_capture_fixture(request, name):
-    fixtures = set(request.fixturenames) & capture_fixtures - {name}
+def _ensure_only_one_capture_fixture(request: FixtureRequest, name):
+    fixtures = sorted(set(request.fixturenames) & capture_fixtures - {name})
     if fixtures:
-        fixtures = sorted(fixtures)
-        fixtures = fixtures[0] if len(fixtures) == 1 else fixtures
+        arg = fixtures[0] if len(fixtures) == 1 else fixtures
         raise request.raiseerror(
-            "cannot use {} and {} at the same time".format(fixtures, name)
+            "cannot use {} and {} at the same time".format(arg, name)
         )
 
 
diff --git a/src/_pytest/doctest.py b/src/_pytest/doctest.py
index db1de1986..48c934e3a 100644
--- a/src/_pytest/doctest.py
+++ b/src/_pytest/doctest.py
@@ -6,8 +6,12 @@ import sys
 import traceback
 import warnings
 from contextlib import contextmanager
+from typing import Dict
+from typing import List
+from typing import Optional
 from typing import Sequence
 from typing import Tuple
+from typing import Union
 
 import pytest
 from _pytest import outcomes
@@ -20,6 +24,10 @@ from _pytest.outcomes import Skipped
 from _pytest.python_api import approx
 from _pytest.warning_types import PytestWarning
 
+if False:  # TYPE_CHECKING
+    import doctest
+    from typing import Type
+
 DOCTEST_REPORT_CHOICE_NONE = "none"
 DOCTEST_REPORT_CHOICE_CDIFF = "cdiff"
 DOCTEST_REPORT_CHOICE_NDIFF = "ndiff"
@@ -36,6 +44,8 @@ DOCTEST_REPORT_CHOICES = (
 
 # Lazy definition of runner class
 RUNNER_CLASS = None
+# Lazy definition of output checker class
+CHECKER_CLASS = None  # type: Optional[Type[doctest.OutputChecker]]
 
 
 def pytest_addoption(parser):
@@ -139,7 +149,7 @@ class MultipleDoctestFailures(Exception):
         self.failures = failures
 
 
-def _init_runner_class():
+def _init_runner_class() -> "Type[doctest.DocTestRunner]":
     import doctest
 
     class PytestDoctestRunner(doctest.DebugRunner):
@@ -177,12 +187,19 @@ def _init_runner_class():
     return PytestDoctestRunner
 
 
-def _get_runner(checker=None, verbose=None, optionflags=0, continue_on_failure=True):
+def _get_runner(
+    checker: Optional["doctest.OutputChecker"] = None,
+    verbose: Optional[bool] = None,
+    optionflags: int = 0,
+    continue_on_failure: bool = True,
+) -> "doctest.DocTestRunner":
     # We need this in order to do a lazy import on doctest
     global RUNNER_CLASS
     if RUNNER_CLASS is None:
         RUNNER_CLASS = _init_runner_class()
-    return RUNNER_CLASS(
+    # Type ignored because the continue_on_failure argument is only defined on
+    # PytestDoctestRunner, which is lazily defined so can't be used as a type.
+    return RUNNER_CLASS(  # type: ignore
         checker=checker,
         verbose=verbose,
         optionflags=optionflags,
@@ -211,7 +228,7 @@ class DoctestItem(pytest.Item):
     def runtest(self):
         _check_all_skipped(self.dtest)
         self._disable_output_capturing_for_darwin()
-        failures = []
+        failures = []  # type: List[doctest.DocTestFailure]
         self.runner.run(self.dtest, out=failures)
         if failures:
             raise MultipleDoctestFailures(failures)
@@ -232,7 +249,9 @@ class DoctestItem(pytest.Item):
     def repr_failure(self, excinfo):
         import doctest
 
-        failures = None
+        failures = (
+            None
+        )  # type: Optional[List[Union[doctest.DocTestFailure, doctest.UnexpectedException]]]
         if excinfo.errisinstance((doctest.DocTestFailure, doctest.UnexpectedException)):
             failures = [excinfo.value]
         elif excinfo.errisinstance(MultipleDoctestFailures):
@@ -255,8 +274,10 @@ class DoctestItem(pytest.Item):
                     self.config.getoption("doctestreport")
                 )
                 if lineno is not None:
+                    assert failure.test.docstring is not None
                     lines = failure.test.docstring.splitlines(False)
                     # add line numbers to the left of the error message
+                    assert test.lineno is not None
                     lines = [
                         "%03d %s" % (i + test.lineno + 1, x)
                         for (i, x) in enumerate(lines)
@@ -288,7 +309,7 @@ class DoctestItem(pytest.Item):
         return self.fspath, self.dtest.lineno, "[doctest] %s" % self.name
 
 
-def _get_flag_lookup():
+def _get_flag_lookup() -> Dict[str, int]:
     import doctest
 
     return dict(
@@ -340,7 +361,7 @@ class DoctestTextfile(pytest.Module):
         optionflags = get_optionflags(self)
 
         runner = _get_runner(
-            verbose=0,
+            verbose=False,
             optionflags=optionflags,
             checker=_get_checker(),
             continue_on_failure=_get_continue_on_failure(self.config),
@@ -419,7 +440,8 @@ class DoctestModule(pytest.Module):
                     return
                 with _patch_unwrap_mock_aware():
 
-                    doctest.DocTestFinder._find(
+                    # Type ignored because this is a private function.
+                    doctest.DocTestFinder._find(  # type: ignore
                         self, tests, obj, name, module, source_lines, globs, seen
                     )
 
@@ -437,7 +459,7 @@ class DoctestModule(pytest.Module):
         finder = MockAwareDocTestFinder()
         optionflags = get_optionflags(self)
         runner = _get_runner(
-            verbose=0,
+            verbose=False,
             optionflags=optionflags,
             checker=_get_checker(),
             continue_on_failure=_get_continue_on_failure(self.config),
@@ -466,24 +488,7 @@ def _setup_fixtures(doctest_item):
     return fixture_request
 
 
-def _get_checker():
-    """
-    Returns a doctest.OutputChecker subclass that supports some
-    additional options:
-
-    * ALLOW_UNICODE and ALLOW_BYTES options to ignore u'' and b''
-      prefixes (respectively) in string literals. Useful when the same
-      doctest should run in Python 2 and Python 3.
-
-    * NUMBER to ignore floating-point differences smaller than the
-      precision of the literal number in the doctest.
-
-    An inner class is used to avoid importing "doctest" at the module
-    level.
-    """
-    if hasattr(_get_checker, "LiteralsOutputChecker"):
-        return _get_checker.LiteralsOutputChecker()
-
+def _init_checker_class() -> "Type[doctest.OutputChecker]":
     import doctest
     import re
 
@@ -573,11 +578,31 @@ def _get_checker():
                     offset += w.end() - w.start() - (g.end() - g.start())
             return got
 
-    _get_checker.LiteralsOutputChecker = LiteralsOutputChecker
-    return _get_checker.LiteralsOutputChecker()
+    return LiteralsOutputChecker
 
 
-def _get_allow_unicode_flag():
+def _get_checker() -> "doctest.OutputChecker":
+    """
+    Returns a doctest.OutputChecker subclass that supports some
+    additional options:
+
+    * ALLOW_UNICODE and ALLOW_BYTES options to ignore u'' and b''
+      prefixes (respectively) in string literals. Useful when the same
+      doctest should run in Python 2 and Python 3.
+
+    * NUMBER to ignore floating-point differences smaller than the
+      precision of the literal number in the doctest.
+
+    An inner class is used to avoid importing "doctest" at the module
+    level.
+    """
+    global CHECKER_CLASS
+    if CHECKER_CLASS is None:
+        CHECKER_CLASS = _init_checker_class()
+    return CHECKER_CLASS()
+
+
+def _get_allow_unicode_flag() -> int:
     """
     Registers and returns the ALLOW_UNICODE flag.
     """
@@ -586,7 +611,7 @@ def _get_allow_unicode_flag():
     return doctest.register_optionflag("ALLOW_UNICODE")
 
 
-def _get_allow_bytes_flag():
+def _get_allow_bytes_flag() -> int:
     """
     Registers and returns the ALLOW_BYTES flag.
     """
@@ -595,7 +620,7 @@ def _get_allow_bytes_flag():
     return doctest.register_optionflag("ALLOW_BYTES")
 
 
-def _get_number_flag():
+def _get_number_flag() -> int:
     """
     Registers and returns the NUMBER flag.
     """
@@ -604,7 +629,7 @@ def _get_number_flag():
     return doctest.register_optionflag("NUMBER")
 
 
-def _get_report_choice(key):
+def _get_report_choice(key: str) -> int:
     """
     This function returns the actual `doctest` module flag value, we want to do it as late as possible to avoid
     importing `doctest` and all its dependencies when parsing options, as it adds overhead and breaks tests.
diff --git a/src/_pytest/logging.py b/src/_pytest/logging.py
index 054bfc866..c72f76118 100644
--- a/src/_pytest/logging.py
+++ b/src/_pytest/logging.py
@@ -2,6 +2,10 @@
 import logging
 import re
 from contextlib import contextmanager
+from typing import AbstractSet
+from typing import Dict
+from typing import List
+from typing import Mapping
 
 import py
 
@@ -32,14 +36,15 @@ class ColoredLevelFormatter(logging.Formatter):
         logging.INFO: {"green"},
         logging.DEBUG: {"purple"},
         logging.NOTSET: set(),
-    }
+    }  # type: Mapping[int, AbstractSet[str]]
     LEVELNAME_FMT_REGEX = re.compile(r"%\(levelname\)([+-.]?\d*s)")
 
-    def __init__(self, terminalwriter, *args, **kwargs):
+    def __init__(self, terminalwriter, *args, **kwargs) -> None:
         super().__init__(*args, **kwargs)
         self._original_fmt = self._style._fmt
-        self._level_to_fmt_mapping = {}
+        self._level_to_fmt_mapping = {}  # type: Dict[int, str]
 
+        assert self._fmt is not None
         levelname_fmt_match = self.LEVELNAME_FMT_REGEX.search(self._fmt)
         if not levelname_fmt_match:
             return
@@ -216,17 +221,17 @@ def catching_logs(handler, formatter=None, level=None):
 class LogCaptureHandler(logging.StreamHandler):
     """A logging handler that stores log records and the log text."""
 
-    def __init__(self):
+    def __init__(self) -> None:
         """Creates a new log handler."""
         logging.StreamHandler.__init__(self, py.io.TextIO())
-        self.records = []
+        self.records = []  # type: List[logging.LogRecord]
 
-    def emit(self, record):
+    def emit(self, record: logging.LogRecord) -> None:
         """Keep the log records in a list in addition to the log text."""
         self.records.append(record)
         logging.StreamHandler.emit(self, record)
 
-    def reset(self):
+    def reset(self) -> None:
         self.records = []
         self.stream = py.io.TextIO()
 
@@ -234,13 +239,13 @@ class LogCaptureHandler(logging.StreamHandler):
 class LogCaptureFixture:
     """Provides access and control of log capturing."""
 
-    def __init__(self, item):
+    def __init__(self, item) -> None:
         """Creates a new funcarg."""
         self._item = item
         # dict of log name -> log level
-        self._initial_log_levels = {}  # Dict[str, int]
+        self._initial_log_levels = {}  # type: Dict[str, int]
 
-    def _finalize(self):
+    def _finalize(self) -> None:
         """Finalizes the fixture.
 
         This restores the log levels changed by :meth:`set_level`.
@@ -453,7 +458,7 @@ class LoggingPlugin:
         ):
             formatter = ColoredLevelFormatter(
                 create_terminal_writer(self._config), log_format, log_date_format
-            )
+            )  # type: logging.Formatter
         else:
             formatter = logging.Formatter(log_format, log_date_format)
 
diff --git a/src/_pytest/nodes.py b/src/_pytest/nodes.py
index e6dee1547..71036dc7e 100644
--- a/src/_pytest/nodes.py
+++ b/src/_pytest/nodes.py
@@ -139,8 +139,7 @@ class Node:
                 )
             )
         path, lineno = get_fslocation_from_item(self)
-        # Type ignored: https://github.com/python/typeshed/pull/3121
-        warnings.warn_explicit(  # type: ignore
+        warnings.warn_explicit(
             warning,
             category=None,
             filename=str(path),
diff --git a/src/_pytest/terminal.py b/src/_pytest/terminal.py
index fd30d8572..35f6d324b 100644
--- a/src/_pytest/terminal.py
+++ b/src/_pytest/terminal.py
@@ -9,6 +9,12 @@ import platform
 import sys
 import time
 from functools import partial
+from typing import Callable
+from typing import Dict
+from typing import List
+from typing import Mapping
+from typing import Optional
+from typing import Set
 
 import attr
 import pluggy
@@ -195,8 +201,8 @@ class WarningReport:
         file system location of the source of the warning (see ``get_location``).
     """
 
-    message = attr.ib()
-    nodeid = attr.ib(default=None)
+    message = attr.ib(type=str)
+    nodeid = attr.ib(type=Optional[str], default=None)
     fslocation = attr.ib(default=None)
     count_towards_summary = True
 
@@ -240,7 +246,7 @@ class TerminalReporter:
         self.reportchars = getreportopt(config)
         self.hasmarkup = self._tw.hasmarkup
         self.isatty = file.isatty()
-        self._progress_nodeids_reported = set()
+        self._progress_nodeids_reported = set()  # type: Set[str]
         self._show_progress_info = self._determine_show_progress_info()
         self._collect_report_last_write = None
 
@@ -619,7 +625,7 @@ class TerminalReporter:
         # because later versions are going to get rid of them anyway
         if self.config.option.verbose < 0:
             if self.config.option.verbose < -1:
-                counts = {}
+                counts = {}  # type: Dict[str, int]
                 for item in items:
                     name = item.nodeid.split("::", 1)[0]
                     counts[name] = counts.get(name, 0) + 1
@@ -750,7 +756,9 @@ class TerminalReporter:
 
     def summary_warnings(self):
         if self.hasopt("w"):
-            all_warnings = self.stats.get("warnings")
+            all_warnings = self.stats.get(
+                "warnings"
+            )  # type: Optional[List[WarningReport]]
             if not all_warnings:
                 return
 
@@ -763,7 +771,9 @@ class TerminalReporter:
             if not warning_reports:
                 return
 
-            reports_grouped_by_message = collections.OrderedDict()
+            reports_grouped_by_message = (
+                collections.OrderedDict()
+            )  # type: collections.OrderedDict[str, List[WarningReport]]
             for wr in warning_reports:
                 reports_grouped_by_message.setdefault(wr.message, []).append(wr)
 
@@ -900,11 +910,11 @@ class TerminalReporter:
         else:
             self.write_line(msg, **main_markup)
 
-    def short_test_summary(self):
+    def short_test_summary(self) -> None:
         if not self.reportchars:
             return
 
-        def show_simple(stat, lines):
+        def show_simple(stat, lines: List[str]) -> None:
             failed = self.stats.get(stat, [])
             if not failed:
                 return
@@ -914,7 +924,7 @@ class TerminalReporter:
                 line = _get_line_with_reprcrash_message(config, rep, termwidth)
                 lines.append(line)
 
-        def show_xfailed(lines):
+        def show_xfailed(lines: List[str]) -> None:
             xfailed = self.stats.get("xfailed", [])
             for rep in xfailed:
                 verbose_word = rep._get_verbose_word(self.config)
@@ -924,7 +934,7 @@ class TerminalReporter:
                 if reason:
                     lines.append("  " + str(reason))
 
-        def show_xpassed(lines):
+        def show_xpassed(lines: List[str]) -> None:
             xpassed = self.stats.get("xpassed", [])
             for rep in xpassed:
                 verbose_word = rep._get_verbose_word(self.config)
@@ -932,7 +942,7 @@ class TerminalReporter:
                 reason = rep.wasxfail
                 lines.append("{} {} {}".format(verbose_word, pos, reason))
 
-        def show_skipped(lines):
+        def show_skipped(lines: List[str]) -> None:
             skipped = self.stats.get("skipped", [])
             fskips = _folded_skips(skipped) if skipped else []
             if not fskips:
@@ -958,9 +968,9 @@ class TerminalReporter:
             "S": show_skipped,
             "p": partial(show_simple, "passed"),
             "E": partial(show_simple, "error"),
-        }
+        }  # type: Mapping[str, Callable[[List[str]], None]]
 
-        lines = []
+        lines = []  # type: List[str]
         for char in self.reportchars:
             action = REPORTCHAR_ACTIONS.get(char)
             if action:  # skipping e.g. "P" (passed with output) here.
@@ -1084,8 +1094,8 @@ def build_summary_stats_line(stats):
     return parts, main_color
 
 
-def _plugin_nameversions(plugininfo):
-    values = []
+def _plugin_nameversions(plugininfo) -> List[str]:
+    values = []  # type: List[str]
     for plugin, dist in plugininfo:
         # gets us name and version!
         name = "{dist.project_name}-{dist.version}".format(dist=dist)
@@ -1099,7 +1109,7 @@ def _plugin_nameversions(plugininfo):
     return values
 
 
-def format_session_duration(seconds):
+def format_session_duration(seconds: float) -> str:
     """Format the given seconds in a human readable manner to show in the final summary"""
     if seconds < 60:
         return "{:.2f}s".format(seconds)
diff --git a/src/_pytest/warnings.py b/src/_pytest/warnings.py
index d817a5cfa..8fdb61c2b 100644
--- a/src/_pytest/warnings.py
+++ b/src/_pytest/warnings.py
@@ -66,6 +66,8 @@ def catch_warnings_for_item(config, ihook, when, item):
     cmdline_filters = config.getoption("pythonwarnings") or []
     inifilters = config.getini("filterwarnings")
     with warnings.catch_warnings(record=True) as log:
+        # mypy can't infer that record=True means log is not None; help it.
+        assert log is not None
 
         if not sys.warnoptions:
             # if user is not explicitly configuring warning filters, show deprecation warnings by default (#2908)
@@ -145,6 +147,8 @@ def _issue_warning_captured(warning, hook, stacklevel):
     with warnings.catch_warnings(record=True) as records:
         warnings.simplefilter("always", type(warning))
         warnings.warn(warning, stacklevel=stacklevel)
+    # Mypy can't infer that record=True means records is not None; help it.
+    assert records is not None
     hook.pytest_warning_captured.call_historic(
         kwargs=dict(warning_message=records[0], when="config", item=None)
     )
diff --git a/testing/test_capture.py b/testing/test_capture.py
index 0f7db4b8e..180637db6 100644
--- a/testing/test_capture.py
+++ b/testing/test_capture.py
@@ -6,6 +6,8 @@ import subprocess
 import sys
 import textwrap
 from io import UnsupportedOperation
+from typing import List
+from typing import TextIO
 
 import py
 
@@ -857,8 +859,8 @@ def tmpfile(testdir):
 
 
 @needsosdup
-def test_dupfile(tmpfile):
-    flist = []
+def test_dupfile(tmpfile) -> None:
+    flist = []  # type: List[TextIO]
     for i in range(5):
         nf = capture.safe_text_dupfile(tmpfile, "wb")
         assert nf != tmpfile
diff --git a/testing/test_doctest.py b/testing/test_doctest.py
index 755f26286..37b3988f7 100644
--- a/testing/test_doctest.py
+++ b/testing/test_doctest.py
@@ -839,7 +839,8 @@ class TestLiterals:
         reprec = testdir.inline_run()
         reprec.assertoutcome(failed=1)
 
-    def test_number_re(self):
+    def test_number_re(self) -> None:
+        _number_re = _get_checker()._number_re  # type: ignore
         for s in [
             "1.",
             "+1.",
@@ -861,12 +862,12 @@ class TestLiterals:
             "-1.2e-3",
         ]:
             print(s)
-            m = _get_checker()._number_re.match(s)
+            m = _number_re.match(s)
             assert m is not None
             assert float(m.group()) == pytest.approx(float(s))
         for s in ["1", "abc"]:
             print(s)
-            assert _get_checker()._number_re.match(s) is None
+            assert _number_re.match(s) is None
 
     @pytest.mark.parametrize("config_mode", ["ini", "comment"])
     def test_number_precision(self, testdir, config_mode):