diff --git a/pandas/core/base.py b/pandas/core/base.py
index ef7e59c9e19d7..d38dbec684f35 100644
--- a/pandas/core/base.py
+++ b/pandas/core/base.py
@@ -8,6 +8,7 @@
 import numpy as np
 
 import pandas._libs.lib as lib
+from pandas._typing import T
 from pandas.compat import PYPY
 from pandas.compat.numpy import function as nv
 from pandas.errors import AbstractMethodError
@@ -87,6 +88,14 @@ def __sizeof__(self):
         # object's 'sizeof'
         return super().__sizeof__()
 
+    def _ensure_type(self: T, obj) -> T:
+        """Ensure that an object has same type as self.
+
+        Used by type checkers.
+        """
+        assert isinstance(obj, type(self)), type(obj)
+        return obj
+
 
 class NoNewAttributesMixin:
     """Mixin which prevents adding new attributes.
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 85bbf9b553b0a..d4e36a1894873 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -19,6 +19,7 @@
     Sequence,
     Set,
     Tuple,
+    Type,
     Union,
 )
 import warnings
@@ -262,7 +263,7 @@ def _validate_dtype(self, dtype):
     # Construction
 
     @property
-    def _constructor(self):
+    def _constructor(self: FrameOrSeries) -> Type[FrameOrSeries]:
         """Used when a manipulation result has the same dimensions as the
         original.
         """
@@ -298,7 +299,7 @@ def _constructor_expanddim(self):
     _AXIS_LEN: int
 
     @classmethod
-    def _setup_axes(cls, axes: List[str], docs: Dict[str, str]):
+    def _setup_axes(cls, axes: List[str], docs: Dict[str, str]) -> None:
         """
         Provide axes setup for the major PandasObjects.
 
@@ -373,7 +374,7 @@ def _construct_axes_from_arguments(
         return axes, kwargs
 
     @classmethod
-    def _from_axes(cls, data, axes, **kwargs):
+    def _from_axes(cls: Type[FrameOrSeries], data, axes, **kwargs) -> FrameOrSeries:
         # for construction from BlockManager
         if isinstance(data, BlockManager):
             return cls(data, **kwargs)
@@ -486,7 +487,7 @@ def shape(self) -> Tuple[int, ...]:
         return tuple(len(self._get_axis(a)) for a in self._AXIS_ORDERS)
 
     @property
-    def axes(self):
+    def axes(self) -> List[Index]:
         """
         Return index label(s) of the internal NDFrame
         """
@@ -639,11 +640,11 @@ def set_axis(self, labels, axis=0, inplace=False):
             obj.set_axis(labels, axis=axis, inplace=True)
             return obj
 
-    def _set_axis(self, axis, labels):
+    def _set_axis(self, axis, labels) -> None:
         self._data.set_axis(axis, labels)
         self._clear_item_cache()
 
-    def swapaxes(self, axis1, axis2, copy=True):
+    def swapaxes(self: FrameOrSeries, axis1, axis2, copy=True) -> FrameOrSeries:
         """
         Interchange axes and swap values axes appropriately.
 
@@ -668,7 +669,7 @@ def swapaxes(self, axis1, axis2, copy=True):
 
         return self._constructor(new_values, *new_axes).__finalize__(self)
 
-    def droplevel(self, level, axis=0):
+    def droplevel(self: FrameOrSeries, level, axis=0) -> FrameOrSeries:
         """
         Return DataFrame with requested index / column level(s) removed.
 
@@ -728,7 +729,7 @@ def droplevel(self, level, axis=0):
         result = self.set_axis(new_labels, axis=axis, inplace=False)
         return result
 
-    def pop(self, item):
+    def pop(self: FrameOrSeries, item) -> FrameOrSeries:
         """
         Return item and drop from frame. Raise KeyError if not found.
 
@@ -889,7 +890,7 @@ def squeeze(self, axis=None):
             )
         ]
 
-    def swaplevel(self, i=-2, j=-1, axis=0):
+    def swaplevel(self: FrameOrSeries, i=-2, j=-1, axis=0) -> FrameOrSeries:
         """
         Swap levels i and j in a MultiIndex on a particular axis
 
@@ -1473,10 +1474,10 @@ def bool(self):
 
         self.__nonzero__()
 
-    def __abs__(self):
+    def __abs__(self: FrameOrSeries) -> FrameOrSeries:
         return self.abs()
 
-    def __round__(self, decimals=0):
+    def __round__(self: FrameOrSeries, decimals: int = 0) -> FrameOrSeries:
         return self.round(decimals)
 
     # -------------------------------------------------------------------------
@@ -2123,7 +2124,7 @@ def to_excel(
         inf_rep="inf",
         verbose=True,
         freeze_panes=None,
-    ):
+    ) -> None:
         df = self if isinstance(self, ABCDataFrame) else self.to_frame()
 
         from pandas.io.formats.excel import ExcelFormatter
@@ -2347,7 +2348,7 @@ def to_hdf(
         data_columns: Optional[List[str]] = None,
         errors: str = "strict",
         encoding: str = "UTF-8",
-    ):
+    ) -> None:
         """
         Write the contained data to an HDF5 file using HDFStore.
 
@@ -2691,7 +2692,9 @@ def to_pickle(
 
         to_pickle(self, path, compression=compression, protocol=protocol)
 
-    def to_clipboard(self, excel: bool_t = True, sep: Optional[str] = None, **kwargs):
+    def to_clipboard(
+        self, excel: bool_t = True, sep: Optional[str] = None, **kwargs
+    ) -> None:
         r"""
         Copy object to the system clipboard.
 
@@ -3259,7 +3262,9 @@ def _clear_item_cache(self) -> None:
     # ----------------------------------------------------------------------
     # Indexing Methods
 
-    def take(self, indices, axis=0, is_copy: bool_t = True, **kwargs):
+    def take(
+        self: FrameOrSeries, indices, axis=0, is_copy: bool_t = True, **kwargs
+    ) -> FrameOrSeries:
         """
         Return the elements in the given *positional* indices along an axis.
 
@@ -3542,7 +3547,7 @@ def _iget_item_cache(self, item):
     def _box_item_values(self, key, values):
         raise AbstractMethodError(self)
 
-    def _slice(self, slobj: slice, axis=0, kind=None):
+    def _slice(self: FrameOrSeries, slobj: slice, axis=0, kind=None) -> FrameOrSeries:
         """
         Construct a slice of this container.
 
@@ -3668,7 +3673,7 @@ def _check_setitem_copy(self, stacklevel=4, t="setting", force=False):
         elif value == "warn":
             warnings.warn(t, com.SettingWithCopyWarning, stacklevel=stacklevel)
 
-    def __delitem__(self, key):
+    def __delitem__(self, key) -> None:
         """
         Delete item
         """
@@ -3730,13 +3735,13 @@ def _is_view(self):
         return self._data.is_view
 
     def reindex_like(
-        self,
+        self: FrameOrSeries,
         other,
         method: Optional[str] = None,
         copy: bool_t = True,
         limit=None,
         tolerance=None,
-    ):
+    ) -> FrameOrSeries:
         """
         Return an object with matching indices as other object.
 
@@ -3878,7 +3883,9 @@ def drop(
         else:
             return obj
 
-    def _drop_axis(self, labels, axis, level=None, errors: str = "raise"):
+    def _drop_axis(
+        self: FrameOrSeries, labels, axis, level=None, errors: str = "raise"
+    ) -> FrameOrSeries:
         """
         Drop labels from specified axis. Used in the ``drop`` method
         internally.
@@ -3948,7 +3955,7 @@ def _update_inplace(self, result, verify_is_copy: bool_t = True) -> None:
         self._data = getattr(result, "_data", result)
         self._maybe_update_cacher(verify_is_copy=verify_is_copy)
 
-    def add_prefix(self, prefix: str):
+    def add_prefix(self: FrameOrSeries, prefix: str) -> FrameOrSeries:
         """
         Prefix labels with string `prefix`.
 
@@ -4007,7 +4014,7 @@ def add_prefix(self, prefix: str):
         mapper = {self._info_axis_name: f}
         return self.rename(**mapper)
 
-    def add_suffix(self, suffix: str):
+    def add_suffix(self: FrameOrSeries, suffix: str) -> FrameOrSeries:
         """
         Suffix labels with string `suffix`.
 
@@ -4227,7 +4234,7 @@ def sort_index(
         new_axis = labels.take(sort_index)
         return self.reindex(**{axis_name: new_axis})
 
-    def reindex(self, *args, **kwargs):
+    def reindex(self: FrameOrSeries, *args, **kwargs) -> FrameOrSeries:
         """
         Conform %(klass)s to new index with optional filling logic.
 
@@ -4475,7 +4482,9 @@ def reindex(self, *args, **kwargs):
             axes, level, limit, tolerance, method, fill_value, copy
         ).__finalize__(self)
 
-    def _reindex_axes(self, axes, level, limit, tolerance, method, fill_value, copy):
+    def _reindex_axes(
+        self: FrameOrSeries, axes, level, limit, tolerance, method, fill_value, copy
+    ) -> FrameOrSeries:
         """Perform the reindex for all the axes."""
         obj = self
         for a in self._AXIS_ORDERS:
@@ -4511,12 +4520,12 @@ def _reindex_multi(self, axes, copy, fill_value):
         raise AbstractMethodError(self)
 
     def _reindex_with_indexers(
-        self,
+        self: FrameOrSeries,
         reindexers,
         fill_value=None,
         copy: bool_t = False,
         allow_dups: bool_t = False,
-    ):
+    ) -> FrameOrSeries:
         """allow_dups indicates an internal call here """
 
         # reindex doing multiple operations on different axes if indicated
@@ -4548,12 +4557,12 @@ def _reindex_with_indexers(
         return self._constructor(new_data).__finalize__(self)
 
     def filter(
-        self,
+        self: FrameOrSeries,
         items=None,
         like: Optional[str] = None,
         regex: Optional[str] = None,
         axis=None,
-    ):
+    ) -> FrameOrSeries:
         """
         Subset the dataframe rows or columns according to the specified index labels.
 
@@ -4793,14 +4802,14 @@ def tail(self: FrameOrSeries, n: int = 5) -> FrameOrSeries:
         return self.iloc[-n:]
 
     def sample(
-        self,
+        self: FrameOrSeries,
         n=None,
         frac=None,
         replace=False,
         weights=None,
         random_state=None,
         axis=None,
-    ):
+    ) -> FrameOrSeries:
         """
         Return a random sample of items from an axis of object.
 
@@ -5339,7 +5348,7 @@ def _get_bool_data(self):
     # Internal Interface Methods
 
     @property
-    def values(self):
+    def values(self) -> np.ndarray:
         """
         Return a Numpy representation of the DataFrame.
 
@@ -5416,16 +5425,16 @@ def values(self):
         return self._data.as_array(transpose=self._AXIS_REVERSED)
 
     @property
-    def _values(self):
+    def _values(self) -> np.ndarray:
         """internal implementation"""
         return self.values
 
     @property
-    def _get_values(self):
+    def _get_values(self) -> np.ndarray:
         # compat
         return self.values
 
-    def _internal_get_values(self):
+    def _internal_get_values(self) -> np.ndarray:
         """
         Return an ndarray after converting sparse values to dense.
 
@@ -5489,7 +5498,9 @@ def _to_dict_of_blocks(self, copy: bool_t = True):
             for k, v, in self._data.to_dict(copy=copy).items()
         }
 
-    def astype(self, dtype, copy: bool_t = True, errors: str = "raise"):
+    def astype(
+        self: FrameOrSeries, dtype, copy: bool_t = True, errors: str = "raise"
+    ) -> FrameOrSeries:
         """
         Cast a pandas object to a specified dtype ``dtype``.
 
@@ -5797,7 +5808,7 @@ def _convert(
             )
         ).__finalize__(self)
 
-    def infer_objects(self):
+    def infer_objects(self: FrameOrSeries) -> FrameOrSeries:
         """
         Attempt to infer better dtypes for object columns.
 
@@ -7054,11 +7065,11 @@ def asof(self, where, subset=None):
         """
 
     @Appender(_shared_docs["isna"] % _shared_doc_kwargs)
-    def isna(self):
+    def isna(self: FrameOrSeries) -> FrameOrSeries:
         return isna(self).__finalize__(self)
 
     @Appender(_shared_docs["isna"] % _shared_doc_kwargs)
-    def isnull(self):
+    def isnull(self: FrameOrSeries) -> FrameOrSeries:
         return isna(self).__finalize__(self)
 
     _shared_docs[
@@ -7124,11 +7135,11 @@ def isnull(self):
         """
 
     @Appender(_shared_docs["notna"] % _shared_doc_kwargs)
-    def notna(self):
+    def notna(self: FrameOrSeries) -> FrameOrSeries:
         return notna(self).__finalize__(self)
 
     @Appender(_shared_docs["notna"] % _shared_doc_kwargs)
-    def notnull(self):
+    def notnull(self: FrameOrSeries) -> FrameOrSeries:
         return notna(self).__finalize__(self)
 
     def _clip_with_scalar(self, lower, upper, inplace: bool_t = False):
@@ -7180,14 +7191,14 @@ def _clip_with_one_bound(self, threshold, method, axis, inplace):
         return self.where(subset, threshold, axis=axis, inplace=inplace)
 
     def clip(
-        self,
+        self: FrameOrSeries,
         lower=None,
         upper=None,
         axis=None,
         inplace: bool_t = False,
         *args,
         **kwargs,
-    ):
+    ) -> FrameOrSeries:
         """
         Trim values at input threshold(s).
 
@@ -7364,13 +7375,13 @@ def clip(
         """
 
     def asfreq(
-        self,
+        self: FrameOrSeries,
         freq,
         method=None,
         how: Optional[str] = None,
         normalize: bool_t = False,
         fill_value=None,
-    ):
+    ) -> FrameOrSeries:
         """
         Convert TimeSeries to specified frequency.
 
@@ -7473,7 +7484,9 @@ def asfreq(
             fill_value=fill_value,
         )
 
-    def at_time(self, time, asof: bool_t = False, axis=None):
+    def at_time(
+        self: FrameOrSeries, time, asof: bool_t = False, axis=None
+    ) -> FrameOrSeries:
         """
         Select values at particular time of day (e.g. 9:30AM).
 
@@ -7530,13 +7543,13 @@ def at_time(self, time, asof: bool_t = False, axis=None):
         return self.take(indexer, axis=axis)
 
     def between_time(
-        self,
+        self: FrameOrSeries,
         start_time,
         end_time,
         include_start: bool_t = True,
         include_end: bool_t = True,
         axis=None,
-    ):
+    ) -> FrameOrSeries:
         """
         Select values between particular times of the day (e.g., 9:00-9:30 AM).
 
@@ -7905,7 +7918,7 @@ def resample(
             level=level,
         )
 
-    def first(self, offset):
+    def first(self: FrameOrSeries, offset) -> FrameOrSeries:
         """
         Method to subset initial periods of time series data based on a date offset.
 
@@ -7967,7 +7980,7 @@ def first(self, offset):
 
         return self.loc[:end]
 
-    def last(self, offset):
+    def last(self: FrameOrSeries, offset) -> FrameOrSeries:
         """
         Method to subset final periods of time series data based on a date offset.
 
@@ -8326,8 +8339,12 @@ def _align_frame(
         )
 
         if method is not None:
-            left = left.fillna(axis=fill_axis, method=method, limit=limit)
-            right = right.fillna(axis=fill_axis, method=method, limit=limit)
+            left = self._ensure_type(
+                left.fillna(method=method, axis=fill_axis, limit=limit)
+            )
+            right = self._ensure_type(
+                right.fillna(method=method, axis=fill_axis, limit=limit)
+            )
 
         # if DatetimeIndex have different tz, convert to UTC
         if is_datetime64tz_dtype(left.index):
@@ -8820,7 +8837,9 @@ def mask(
     """
 
     @Appender(_shared_docs["shift"] % _shared_doc_kwargs)
-    def shift(self, periods=1, freq=None, axis=0, fill_value=None):
+    def shift(
+        self: FrameOrSeries, periods=1, freq=None, axis=0, fill_value=None
+    ) -> FrameOrSeries:
         if periods == 0:
             return self.copy()
 
@@ -8871,7 +8890,9 @@ def slice_shift(self: FrameOrSeries, periods: int = 1, axis=0) -> FrameOrSeries:
 
         return new_obj.__finalize__(self)
 
-    def tshift(self, periods: int = 1, freq=None, axis=0):
+    def tshift(
+        self: FrameOrSeries, periods: int = 1, freq=None, axis=0
+    ) -> FrameOrSeries:
         """
         Shift the time index, using the index's frequency if available.
 
@@ -9314,7 +9335,7 @@ def _tz_localize(ax, tz, ambiguous, nonexistent):
 
     # ----------------------------------------------------------------------
     # Numeric Methods
-    def abs(self):
+    def abs(self: FrameOrSeries) -> FrameOrSeries:
         """
         Return a Series/DataFrame with absolute numeric value of each element.
 
@@ -9383,7 +9404,9 @@ def abs(self):
         """
         return np.abs(self)
 
-    def describe(self, percentiles=None, include=None, exclude=None):
+    def describe(
+        self: FrameOrSeries, percentiles=None, include=None, exclude=None
+    ) -> FrameOrSeries:
         """
         Generate descriptive statistics.
 
@@ -9719,7 +9742,7 @@ def describe_1d(data):
 
         ldesc = [describe_1d(s) for _, s in data.items()]
         # set a convenient order for rows
-        names = []
+        names: List[Optional[Hashable]] = []
         ldesc_indexes = sorted((x.index for x in ldesc), key=len)
         for idxnames in ldesc_indexes:
             for name in idxnames:
@@ -9848,13 +9871,22 @@ def describe_1d(data):
         """
 
     @Appender(_shared_docs["pct_change"] % _shared_doc_kwargs)
-    def pct_change(self, periods=1, fill_method="pad", limit=None, freq=None, **kwargs):
+    def pct_change(
+        self: FrameOrSeries,
+        periods=1,
+        fill_method="pad",
+        limit=None,
+        freq=None,
+        **kwargs,
+    ) -> FrameOrSeries:
         # TODO: Not sure if above is correct - need someone to confirm.
         axis = self._get_axis_number(kwargs.pop("axis", self._stat_axis_name))
         if fill_method is None:
             data = self
         else:
-            data = self.fillna(method=fill_method, limit=limit, axis=axis)
+            data = self._ensure_type(
+                self.fillna(method=fill_method, axis=axis, limit=limit)
+            )
 
         rs = data.div(data.shift(periods=periods, freq=freq, axis=axis, **kwargs)) - 1
         rs = rs.loc[~rs.index.duplicated()]
diff --git a/pandas/core/reshape/pivot.py b/pandas/core/reshape/pivot.py
index 2eb2990bd58c4..c544c132d6921 100644
--- a/pandas/core/reshape/pivot.py
+++ b/pandas/core/reshape/pivot.py
@@ -148,9 +148,7 @@ def pivot_table(
         table = table.sort_index(axis=1)
 
     if fill_value is not None:
-        filled = table.fillna(value=fill_value, downcast="infer")
-        assert filled is not None  # needed for mypy
-        table = filled
+        table = table._ensure_type(table.fillna(fill_value, downcast="infer"))
 
     if margins:
         if dropna: