diff --git a/luigi/configuration/cfg_parser.py b/luigi/configuration/cfg_parser.py
index abca6d713a..ceb51e99ae 100644
--- a/luigi/configuration/cfg_parser.py
+++ b/luigi/configuration/cfg_parser.py
@@ -117,7 +117,7 @@ def before_write(self, parser, section, option, value):
 class LuigiConfigParser(BaseParser, ConfigParser):
     NO_DEFAULT = object()
     enabled = True
-    optionxform = str
+    optionxform = str  # type: ignore
     _instance = None
     _config_paths = [
         '/etc/luigi/client.cfg',  # Deprecated old-style global luigi config
diff --git a/luigi/configuration/toml_parser.py b/luigi/configuration/toml_parser.py
index 683d8b5c4b..0d977e6ecc 100644
--- a/luigi/configuration/toml_parser.py
+++ b/luigi/configuration/toml_parser.py
@@ -16,11 +16,13 @@
 #
 import os.path
 from configparser import ConfigParser
+from typing import Any, Dict
 
 try:
     import toml
+    toml_enabled = True
 except ImportError:
-    toml = False
+    toml_enabled = False
 
 from .base_parser import BaseParser
 from ..freezing import recursively_freeze
@@ -28,8 +30,8 @@
 
 class LuigiTomlParser(BaseParser, ConfigParser):
     NO_DEFAULT = object()
-    enabled = bool(toml)
-    data = dict()
+    enabled = bool(toml_enabled)
+    data: Dict[str, Any] = dict()
     _instance = None
     _config_paths = [
         '/etc/luigi/luigi.toml',
diff --git a/luigi/db_task_history.py b/luigi/db_task_history.py
index e1eabcb7d1..69dc65d63c 100644
--- a/luigi/db_task_history.py
+++ b/luigi/db_task_history.py
@@ -188,7 +188,7 @@ def find_task_by_id(self, id, session=None):
             return session.query(TaskRecord).get(id)
 
 
-class TaskParameter(Base):
+class TaskParameter(Base):  # type: ignore
     """
     Table to track luigi.Parameter()s of a Task.
     """
@@ -201,7 +201,7 @@ def __repr__(self):
         return "TaskParameter(task_id=%d, name=%s, value=%s)" % (self.task_id, self.name, self.value)
 
 
-class TaskEvent(Base):
+class TaskEvent(Base):  # type: ignore
     """
     Table to track when a task is scheduled, starts, finishes, and fails.
     """
@@ -215,7 +215,7 @@ def __repr__(self):
         return "TaskEvent(task_id=%s, event_name=%s, ts=%s" % (self.task_id, self.event_name, self.ts)
 
 
-class TaskRecord(Base):
+class TaskRecord(Base):  # type: ignore
     """
     Base table to track information about a luigi.Task.
 
diff --git a/luigi/freezing.py b/luigi/freezing.py
index 2f0a4b49f6..037e574b92 100644
--- a/luigi/freezing.py
+++ b/luigi/freezing.py
@@ -8,7 +8,7 @@
 try:
     from collections.abc import Mapping
 except ImportError:
-    from collections import Mapping
+    from collections import Mapping  # type: ignore
 import operator
 import functools
 
diff --git a/luigi/parameter.py b/luigi/parameter.py
index f7f137a6d1..83b21ff24b 100644
--- a/luigi/parameter.py
+++ b/luigi/parameter.py
@@ -1603,4 +1603,4 @@ def normalize(self, x):
 class OptionalPathParameter(OptionalParameter, PathParameter):
     """Class to parse optional path parameters."""
 
-    expected_type = (str, Path)
+    expected_type = (str, Path)  # type: ignore
diff --git a/luigi/scheduler.py b/luigi/scheduler.py
index 10d67a10af..81532d3c96 100644
--- a/luigi/scheduler.py
+++ b/luigi/scheduler.py
@@ -84,7 +84,7 @@
     "disable_hard_timeout",
     "disable_window",
 ]
-RetryPolicy = collections.namedtuple("RetryPolicy", _retry_policy_fields)
+RetryPolicy = collections.namedtuple("RetryPolicy", _retry_policy_fields)  # type: ignore
 
 
 def _get_empty_retry_policy():
diff --git a/luigi/task.py b/luigi/task.py
index 4d3a312884..3482f1bf26 100644
--- a/luigi/task.py
+++ b/luigi/task.py
@@ -29,6 +29,7 @@
 import re
 import copy
 import functools
+from typing import Any, Dict
 
 import luigi
 
@@ -170,7 +171,7 @@ class MyTask(luigi.Task):
 
     """
 
-    _event_callbacks = {}
+    _event_callbacks: Dict[Any, Any] = {}
 
     #: Priority of the task: the scheduler should favor available
     #: tasks with higher priority values first.
@@ -180,7 +181,7 @@ class MyTask(luigi.Task):
 
     #: Resources used by the task. Should be formatted like {"scp": 1} to indicate that the
     #: task requires 1 unit of the scp resource.
-    resources = {}
+    resources: Dict[str, Any] = {}
 
     #: Number of seconds after which to time out the run function.
     #: No timeout if set to 0.
diff --git a/luigi/task_register.py b/luigi/task_register.py
index f5e0acdd32..c9d462a56b 100644
--- a/luigi/task_register.py
+++ b/luigi/task_register.py
@@ -19,8 +19,9 @@
 """
 
 import abc
-
 import logging
+from typing import Any, Dict, List
+
 logger = logging.getLogger('luigi-interface')
 
 
@@ -46,9 +47,9 @@ class Register(abc.ABCMeta):
        same object.
     2. Keep track of all subclasses of :py:class:`Task` and expose them.
     """
-    __instance_cache = {}
-    _default_namespace_dict = {}
-    _reg = []
+    __instance_cache: Dict[str, Any] = {}
+    _default_namespace_dict: Dict[str, Any] = {}
+    _reg: List[Any] = []
     AMBIGUOUS_CLASS = object()  # Placeholder denoting an error
     """If this value is returned by :py:meth:`_get_reg` then there is an
     ambiguous task name (two :py:class:`Task` have the same name). This denotes
diff --git a/tox.ini b/tox.ini
index f9e93d6889..0e3f3e0f5d 100644
--- a/tox.ini
+++ b/tox.ini
@@ -62,6 +62,9 @@ deps =
     dropbox: dropbox>=11.0.0
     jsonschema
     mypy
+    types-toml
+    types-python-dateutil
+    types-requests
 passenv =
     USER JAVA_HOME POSTGRES_USER DATAPROC_TEST_PROJECT_ID GCS_TEST_PROJECT_ID GCS_TEST_BUCKET GOOGLE_APPLICATION_CREDENTIALS TRAVIS_BUILD_ID TRAVIS TRAVIS_BRANCH TRAVIS_JOB_NUMBER TRAVIS_PULL_REQUEST TRAVIS_JOB_ID TRAVIS_REPO_SLUG TRAVIS_COMMIT CI DROPBOX_APP_TOKEN DOCKERHUB_TOKEN GITHUB_ACTIONS OVERRIDE_SKIP_CI_TESTS
 setenv =