diff --git a/pandas/_config/config.py b/pandas/_config/config.py
index 42df8a84a8c77..cacd6f5454de7 100644
--- a/pandas/_config/config.py
+++ b/pandas/_config/config.py
@@ -51,7 +51,18 @@
 from collections import namedtuple
 from contextlib import contextmanager
 import re
-from typing import Any, Dict, Iterable, List
+from typing import (
+    Any,
+    Callable,
+    Dict,
+    Iterable,
+    List,
+    Optional,
+    Tuple,
+    Type,
+    TypeVar,
+    cast,
+)
 import warnings
 
 DeprecatedOption = namedtuple("DeprecatedOption", "key msg rkey removal_ver")
@@ -80,7 +91,7 @@ class OptionError(AttributeError, KeyError):
 # User API
 
 
-def _get_single_key(pat, silent):
+def _get_single_key(pat: str, silent: bool) -> str:
     keys = _select_options(pat)
     if len(keys) == 0:
         if not silent:
@@ -98,7 +109,7 @@ def _get_single_key(pat, silent):
     return key
 
 
-def _get_option(pat, silent=False):
+def _get_option(pat: str, silent: bool = False):
     key = _get_single_key(pat, silent)
 
     # walk the nested dict
@@ -106,7 +117,7 @@ def _get_option(pat, silent=False):
     return root[k]
 
 
-def _set_option(*args, **kwargs):
+def _set_option(*args, **kwargs) -> None:
     # must at least 1 arg deal with constraints later
     nargs = len(args)
     if not nargs or nargs % 2 != 0:
@@ -138,7 +149,7 @@ def _set_option(*args, **kwargs):
                 o.cb(key)
 
 
-def _describe_option(pat="", _print_desc=True):
+def _describe_option(pat: str = "", _print_desc: bool = True):
 
     keys = _select_options(pat)
     if len(keys) == 0:
@@ -154,7 +165,7 @@ def _describe_option(pat="", _print_desc=True):
         return s
 
 
-def _reset_option(pat, silent=False):
+def _reset_option(pat: str, silent: bool = False) -> None:
 
     keys = _select_options(pat)
 
@@ -172,7 +183,7 @@ def _reset_option(pat, silent=False):
         _set_option(k, _registered_options[k].defval, silent=silent)
 
 
-def get_default_val(pat):
+def get_default_val(pat: str):
     key = _get_single_key(pat, silent=True)
     return _get_registered_option(key).defval
 
@@ -180,11 +191,11 @@ def get_default_val(pat):
 class DictWrapper:
     """ provide attribute-style access to a nested dict"""
 
-    def __init__(self, d, prefix=""):
+    def __init__(self, d: Dict[str, Any], prefix: str = ""):
         object.__setattr__(self, "d", d)
         object.__setattr__(self, "prefix", prefix)
 
-    def __setattr__(self, key, val):
+    def __setattr__(self, key: str, val: Any) -> None:
         prefix = object.__getattribute__(self, "prefix")
         if prefix:
             prefix += "."
@@ -210,7 +221,7 @@ def __getattr__(self, key: str):
         else:
             return _get_option(prefix)
 
-    def __dir__(self):
+    def __dir__(self) -> Iterable[str]:
         return list(self.d.keys())
 
 
@@ -411,23 +422,31 @@ def __exit__(self, *args):
                 _set_option(pat, val, silent=True)
 
 
-def register_option(key: str, defval: object, doc="", validator=None, cb=None):
-    """Register an option in the package-wide pandas config object
+def register_option(
+    key: str,
+    defval: object,
+    doc: str = "",
+    validator: Optional[Callable[[Any], Any]] = None,
+    cb: Optional[Callable[[str], Any]] = None,
+) -> None:
+    """
+    Register an option in the package-wide pandas config object
 
     Parameters
     ----------
-    key       - a fully-qualified key, e.g. "x.y.option - z".
-    defval    - the default value of the option
-    doc       - a string description of the option
-    validator - a function of a single argument, should raise `ValueError` if
-                called with a value which is not a legal value for the option.
-    cb        - a function of a single argument "key", which is called
-                immediately after an option value is set/reset. key is
-                the full name of the option.
-
-    Returns
-    -------
-    Nothing.
+    key : str
+        Fully-qualified key, e.g. "x.y.option - z".
+    defval : object
+        Default value of the option.
+    doc : str
+        Description of the option.
+    validator : Callable, optional
+        Function of a single argument, should raise `ValueError` if
+        called with a value which is not a legal value for the option.
+    cb
+        a function of a single argument "key", which is called
+        immediately after an option value is set/reset. key is
+        the full name of the option.
 
     Raises
     ------
@@ -480,7 +499,9 @@ def register_option(key: str, defval: object, doc="", validator=None, cb=None):
     )
 
 
-def deprecate_option(key, msg=None, rkey=None, removal_ver=None):
+def deprecate_option(
+    key: str, msg: Optional[str] = None, rkey: Optional[str] = None, removal_ver=None
+) -> None:
     """
     Mark option `key` as deprecated, if code attempts to access this option,
     a warning will be produced, using `msg` if given, or a default message
@@ -493,32 +514,27 @@ def deprecate_option(key, msg=None, rkey=None, removal_ver=None):
 
     Parameters
     ----------
-    key - the name of the option to be deprecated. must be a fully-qualified
-          option name (e.g "x.y.z.rkey").
-
-    msg - (Optional) a warning message to output when the key is referenced.
-          if no message is given a default message will be emitted.
-
-    rkey - (Optional) the name of an option to reroute access to.
-           If specified, any referenced `key` will be re-routed to `rkey`
-           including set/get/reset.
-           rkey must be a fully-qualified option name (e.g "x.y.z.rkey").
-           used by the default message if no `msg` is specified.
-
-    removal_ver - (Optional) specifies the version in which this option will
-                  be removed. used by the default message if no `msg`
-                  is specified.
-
-    Returns
-    -------
-    Nothing
+    key : str
+        Name of the option to be deprecated.
+        must be a fully-qualified option name (e.g "x.y.z.rkey").
+    msg : str, optional
+        Warning message to output when the key is referenced.
+        if no message is given a default message will be emitted.
+    rkey : str, optional
+        Name of an option to reroute access to.
+        If specified, any referenced `key` will be
+        re-routed to `rkey` including set/get/reset.
+        rkey must be a fully-qualified option name (e.g "x.y.z.rkey").
+        used by the default message if no `msg` is specified.
+    removal_ver : optional
+        Specifies the version in which this option will
+        be removed. used by the default message if no `msg` is specified.
 
     Raises
     ------
-    OptionError - if key has already been deprecated.
-
+    OptionError
+        If the specified key has already been deprecated.
     """
-
     key = key.lower()
 
     if key in _deprecated_options:
@@ -531,7 +547,7 @@ def deprecate_option(key, msg=None, rkey=None, removal_ver=None):
 # functions internal to the module
 
 
-def _select_options(pat):
+def _select_options(pat: str) -> List[str]:
     """returns a list of keys matching `pat`
 
     if pat=="all", returns all registered options
@@ -549,7 +565,7 @@ def _select_options(pat):
     return [k for k in keys if re.search(pat, k, re.I)]
 
 
-def _get_root(key):
+def _get_root(key: str) -> Tuple[Dict[str, Any], str]:
     path = key.split(".")
     cursor = _global_config
     for p in path[:-1]:
@@ -557,14 +573,14 @@ def _get_root(key):
     return cursor, path[-1]
 
 
-def _is_deprecated(key):
+def _is_deprecated(key: str) -> bool:
     """ Returns True if the given option has been deprecated """
 
     key = key.lower()
     return key in _deprecated_options
 
 
-def _get_deprecated_option(key):
+def _get_deprecated_option(key: str):
     """
     Retrieves the metadata for a deprecated option, if `key` is deprecated.
 
@@ -581,7 +597,7 @@ def _get_deprecated_option(key):
         return d
 
 
-def _get_registered_option(key):
+def _get_registered_option(key: str):
     """
     Retrieves the option metadata if `key` is a registered option.
 
@@ -592,7 +608,7 @@ def _get_registered_option(key):
     return _registered_options.get(key)
 
 
-def _translate_key(key):
+def _translate_key(key: str) -> str:
     """
     if key id deprecated and a replacement key defined, will return the
     replacement key, otherwise returns `key` as - is
@@ -605,7 +621,7 @@ def _translate_key(key):
         return key
 
 
-def _warn_if_deprecated(key):
+def _warn_if_deprecated(key: str) -> bool:
     """
     Checks if `key` is a deprecated option and if so, prints a warning.
 
@@ -633,7 +649,7 @@ def _warn_if_deprecated(key):
     return False
 
 
-def _build_option_description(k):
+def _build_option_description(k: str) -> str:
     """ Builds a formatted description of a registered option and prints it """
 
     o = _get_registered_option(k)
@@ -658,7 +674,7 @@ def _build_option_description(k):
     return s
 
 
-def pp_options_list(keys, width=80, _print=False):
+def pp_options_list(keys: Iterable[str], width=80, _print: bool = False):
     """ Builds a concise listing of available options, grouped by prefix """
 
     from textwrap import wrap
@@ -696,6 +712,9 @@ def pp(name: str, ks: Iterable[str]) -> List[str]:
 #
 # helpers
 
+FuncType = Callable[..., Any]
+F = TypeVar("F", bound=FuncType)
+
 
 @contextmanager
 def config_prefix(prefix):
@@ -727,12 +746,12 @@ def config_prefix(prefix):
 
     global register_option, get_option, set_option, reset_option
 
-    def wrap(func):
-        def inner(key, *args, **kwds):
+    def wrap(func: F) -> F:
+        def inner(key: str, *args, **kwds):
             pkey = f"{prefix}.{key}"
             return func(pkey, *args, **kwds)
 
-        return inner
+        return cast(F, inner)
 
     _register_option = register_option
     _get_option = get_option
@@ -750,7 +769,7 @@ def inner(key, *args, **kwds):
 # arg in register_option
 
 
-def is_type_factory(_type):
+def is_type_factory(_type: Type[Any]) -> Callable[[Any], None]:
     """
 
     Parameters
@@ -764,14 +783,14 @@ def is_type_factory(_type):
 
     """
 
-    def inner(x):
+    def inner(x) -> None:
         if type(x) != _type:
             raise ValueError(f"Value must have type '{_type}'")
 
     return inner
 
 
-def is_instance_factory(_type):
+def is_instance_factory(_type) -> Callable[[Any], None]:
     """
 
     Parameters
@@ -791,19 +810,19 @@ def is_instance_factory(_type):
     else:
         type_repr = f"'{_type}'"
 
-    def inner(x):
+    def inner(x) -> None:
         if not isinstance(x, _type):
             raise ValueError(f"Value must be an instance of {type_repr}")
 
     return inner
 
 
-def is_one_of_factory(legal_values):
+def is_one_of_factory(legal_values) -> Callable[[Any], None]:
 
     callables = [c for c in legal_values if callable(c)]
     legal_values = [c for c in legal_values if not callable(c)]
 
-    def inner(x):
+    def inner(x) -> None:
         if x not in legal_values:
 
             if not any(c(x) for c in callables):
@@ -817,7 +836,7 @@ def inner(x):
     return inner
 
 
-def is_nonnegative_int(value):
+def is_nonnegative_int(value: Optional[int]) -> None:
     """
     Verify that value is None or a positive int.
 
@@ -852,7 +871,7 @@ def is_nonnegative_int(value):
 is_text = is_instance_factory((str, bytes))
 
 
-def is_callable(obj):
+def is_callable(obj) -> bool:
     """
 
     Parameters
diff --git a/pandas/core/apply.py b/pandas/core/apply.py
index 14a3c3c008e92..ca1be3154757a 100644
--- a/pandas/core/apply.py
+++ b/pandas/core/apply.py
@@ -1,10 +1,11 @@
 import abc
 import inspect
-from typing import TYPE_CHECKING, Any, Dict, Iterator, Tuple, Type, Union
+from typing import TYPE_CHECKING, Any, Dict, Iterator, Optional, Tuple, Type, Union
 
 import numpy as np
 
 from pandas._libs import reduction as libreduction
+from pandas._typing import Axis
 from pandas.util._decorators import cache_readonly
 
 from pandas.core.dtypes.common import (
@@ -26,9 +27,9 @@
 def frame_apply(
     obj: "DataFrame",
     func,
-    axis=0,
+    axis: Axis = 0,
     raw: bool = False,
-    result_type=None,
+    result_type: Optional[str] = None,
     ignore_failures: bool = False,
     args=None,
     kwds=None,
@@ -87,7 +88,7 @@ def __init__(
         obj: "DataFrame",
         func,
         raw: bool,
-        result_type,
+        result_type: Optional[str],
         ignore_failures: bool,
         args,
         kwds,
diff --git a/pandas/core/construction.py b/pandas/core/construction.py
index 203ef3ec75c8f..f947a1fda49f1 100644
--- a/pandas/core/construction.py
+++ b/pandas/core/construction.py
@@ -334,7 +334,7 @@ def array(
     return result
 
 
-def extract_array(obj, extract_numpy=False):
+def extract_array(obj, extract_numpy: bool = False):
     """
     Extract the ndarray or ExtensionArray from a Series or Index.