diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index ef561d50066d1..f60aa6e4f26b1 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -211,6 +211,7 @@ Removal of prior version deprecations/changes
 - Enforced deprecation of strings ``T``, ``L``, ``U``, and ``N`` denoting frequencies in :class:`Minute`, :class:`Second`, :class:`Milli`, :class:`Micro`, :class:`Nano` (:issue:`57627`)
 - Enforced deprecation of strings ``T``, ``L``, ``U``, and ``N`` denoting units in :class:`Timedelta` (:issue:`57627`)
 - Enforced deprecation of the behavior of :func:`concat` when ``len(keys) != len(objs)`` would truncate to the shorter of the two. Now this raises a ``ValueError`` (:issue:`43485`)
+- Enforced deprecation of values "pad", "ffill", "bfill", and "backfill" for :meth:`Series.interpolate` and :meth:`DataFrame.interpolate` (:issue:`57869`)
 - Enforced silent-downcasting deprecation for :ref:`all relevant methods <whatsnew_220.silent_downcasting>` (:issue:`54710`)
 - In :meth:`DataFrame.stack`, the default value of ``future_stack`` is now ``True``; specifying ``False`` will raise a ``FutureWarning`` (:issue:`55448`)
 - Iterating over a :class:`.DataFrameGroupBy` or :class:`.SeriesGroupBy` will return tuples of length 1 for the groups when grouping by ``level`` a list of length 1 (:issue:`50064`)
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index c9e6ffe1d7dc6..c0eda7f022d8f 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -7624,7 +7624,6 @@ def interpolate(
             * 'time': Works on daily and higher resolution data to interpolate
               given length of interval.
             * 'index', 'values': use the actual numerical values of the index.
-            * 'pad': Fill in NaNs using existing values.
             * 'nearest', 'zero', 'slinear', 'quadratic', 'cubic',
               'barycentric', 'polynomial': Passed to
               `scipy.interpolate.interp1d`, whereas 'spline' is passed to
@@ -7648,23 +7647,9 @@ def interpolate(
             0.
         inplace : bool, default False
             Update the data in place if possible.
-        limit_direction : {{'forward', 'backward', 'both'}}, Optional
+        limit_direction : {{'forward', 'backward', 'both'}}, optional, default 'forward'
             Consecutive NaNs will be filled in this direction.
 
-            If limit is specified:
-                * If 'method' is 'pad' or 'ffill', 'limit_direction' must be 'forward'.
-                * If 'method' is 'backfill' or 'bfill', 'limit_direction' must be
-                  'backwards'.
-
-            If 'limit' is not specified:
-                * If 'method' is 'backfill' or 'bfill', the default is 'backward'
-                * else the default is 'forward'
-
-            raises ValueError if `limit_direction` is 'forward' or 'both' and
-                method is 'backfill' or 'bfill'.
-            raises ValueError if `limit_direction` is 'backward' or 'both' and
-                method is 'pad' or 'ffill'.
-
         limit_area : {{`None`, 'inside', 'outside'}}, default None
             If limit is specified, consecutive NaNs will be filled with this
             restriction.
@@ -7797,30 +7782,11 @@ def interpolate(
         if not isinstance(method, str):
             raise ValueError("'method' should be a string, not None.")
 
-        fillna_methods = ["ffill", "bfill", "pad", "backfill"]
-        if method.lower() in fillna_methods:
-            # GH#53581
-            warnings.warn(
-                f"{type(self).__name__}.interpolate with method={method} is "
-                "deprecated and will raise in a future version. "
-                "Use obj.ffill() or obj.bfill() instead.",
-                FutureWarning,
-                stacklevel=find_stack_level(),
-            )
-            obj, should_transpose = self, False
-        else:
-            obj, should_transpose = (self.T, True) if axis == 1 else (self, False)
-            # GH#53631
-            if np.any(obj.dtypes == object):
-                raise TypeError(
-                    f"{type(self).__name__} cannot interpolate with object dtype."
-                )
-
-        if method in fillna_methods and "fill_value" in kwargs:
-            raise ValueError(
-                "'fill_value' is not a valid keyword for "
-                f"{type(self).__name__}.interpolate with method from "
-                f"{fillna_methods}"
+        obj, should_transpose = (self.T, True) if axis == 1 else (self, False)
+        # GH#53631
+        if np.any(obj.dtypes == object):
+            raise TypeError(
+                f"{type(self).__name__} cannot interpolate with object dtype."
             )
 
         if isinstance(obj.index, MultiIndex) and method != "linear":
@@ -7830,34 +7796,16 @@ def interpolate(
 
         limit_direction = missing.infer_limit_direction(limit_direction, method)
 
-        if method.lower() in fillna_methods:
-            # TODO(3.0): remove this case
-            # TODO: warn/raise on limit_direction or kwargs which are ignored?
-            #  as of 2023-06-26 no tests get here with either
-            if not self._mgr.is_single_block and axis == 1:
-                # GH#53898
-                if inplace:
-                    raise NotImplementedError()
-                obj, axis, should_transpose = self.T, 1 - axis, True
-
-            new_data = obj._mgr.pad_or_backfill(
-                method=method,
-                axis=self._get_block_manager_axis(axis),
-                limit=limit,
-                limit_area=limit_area,
-                inplace=inplace,
-            )
-        else:
-            index = missing.get_interp_index(method, obj.index)
-            new_data = obj._mgr.interpolate(
-                method=method,
-                index=index,
-                limit=limit,
-                limit_direction=limit_direction,
-                limit_area=limit_area,
-                inplace=inplace,
-                **kwargs,
-            )
+        index = missing.get_interp_index(method, obj.index)
+        new_data = obj._mgr.interpolate(
+            method=method,
+            index=index,
+            limit=limit,
+            limit_direction=limit_direction,
+            limit_area=limit_area,
+            inplace=inplace,
+            **kwargs,
+        )
 
         result = self._constructor_from_mgr(new_data, axes=new_data.axes)
         if should_transpose:
diff --git a/pandas/core/missing.py b/pandas/core/missing.py
index de26ad14a7b7a..b3e152e36a304 100644
--- a/pandas/core/missing.py
+++ b/pandas/core/missing.py
@@ -322,13 +322,17 @@ def get_interp_index(method, index: Index) -> Index:
             or isinstance(index.dtype, DatetimeTZDtype)
             or lib.is_np_dtype(index.dtype, "mM")
         )
-        if method not in methods and not is_numeric_or_datetime:
-            raise ValueError(
-                "Index column must be numeric or datetime type when "
-                f"using {method} method other than linear. "
-                "Try setting a numeric or datetime index column before "
-                "interpolating."
-            )
+        valid = NP_METHODS + SP_METHODS
+        if method in valid:
+            if method not in methods and not is_numeric_or_datetime:
+                raise ValueError(
+                    "Index column must be numeric or datetime type when "
+                    f"using {method} method other than linear. "
+                    "Try setting a numeric or datetime index column before "
+                    "interpolating."
+                )
+        else:
+            raise ValueError(f"Can not interpolate with method={method}.")
 
     if isna(index).any():
         raise NotImplementedError(
@@ -611,7 +615,9 @@ def _interpolate_scipy_wrapper(
             y = y.copy()
         if not new_x.flags.writeable:
             new_x = new_x.copy()
-        terp = alt_methods[method]
+        terp = alt_methods.get(method, None)
+        if terp is None:
+            raise ValueError(f"Can not interpolate with method={method}.")
         new_y = terp(x, y, new_x, **kwargs)
     return new_y
 
diff --git a/pandas/tests/copy_view/test_interp_fillna.py b/pandas/tests/copy_view/test_interp_fillna.py
index 8fe58e59b9cfd..abd87162ec32e 100644
--- a/pandas/tests/copy_view/test_interp_fillna.py
+++ b/pandas/tests/copy_view/test_interp_fillna.py
@@ -19,19 +19,18 @@ def test_interpolate_no_op(method):
     df = DataFrame({"a": [1, 2]})
     df_orig = df.copy()
 
-    warn = None
     if method == "pad":
-        warn = FutureWarning
-    msg = "DataFrame.interpolate with method=pad is deprecated"
-    with tm.assert_produces_warning(warn, match=msg):
+        msg = f"Can not interpolate with method={method}"
+        with pytest.raises(ValueError, match=msg):
+            df.interpolate(method=method)
+    else:
         result = df.interpolate(method=method)
+        assert np.shares_memory(get_array(result, "a"), get_array(df, "a"))
 
-    assert np.shares_memory(get_array(result, "a"), get_array(df, "a"))
+        result.iloc[0, 0] = 100
 
-    result.iloc[0, 0] = 100
-
-    assert not np.shares_memory(get_array(result, "a"), get_array(df, "a"))
-    tm.assert_frame_equal(df, df_orig)
+        assert not np.shares_memory(get_array(result, "a"), get_array(df, "a"))
+        tm.assert_frame_equal(df, df_orig)
 
 
 @pytest.mark.parametrize("func", ["ffill", "bfill"])
@@ -122,9 +121,6 @@ def test_interpolate_cannot_with_object_dtype():
 def test_interpolate_object_convert_no_op():
     df = DataFrame({"a": ["a", "b", "c"], "b": 1})
     arr_a = get_array(df, "a")
-    msg = "DataFrame.interpolate with method=pad is deprecated"
-    with tm.assert_produces_warning(FutureWarning, match=msg):
-        df.interpolate(method="pad", inplace=True)
 
     # Now CoW makes a copy, it should not!
     assert df._mgr._has_no_reference(0)
@@ -134,8 +130,8 @@ def test_interpolate_object_convert_no_op():
 def test_interpolate_object_convert_copies():
     df = DataFrame({"a": [1, np.nan, 2.5], "b": 1})
     arr_a = get_array(df, "a")
-    msg = "DataFrame.interpolate with method=pad is deprecated"
-    with tm.assert_produces_warning(FutureWarning, match=msg):
+    msg = "Can not interpolate with method=pad"
+    with pytest.raises(ValueError, match=msg):
         df.interpolate(method="pad", inplace=True, downcast="infer")
 
     assert df._mgr._has_no_reference(0)
@@ -147,12 +143,13 @@ def test_interpolate_downcast_reference_triggers_copy():
     df_orig = df.copy()
     arr_a = get_array(df, "a")
     view = df[:]
-    msg = "DataFrame.interpolate with method=pad is deprecated"
-    with tm.assert_produces_warning(FutureWarning, match=msg):
+
+    msg = "Can not interpolate with method=pad"
+    with pytest.raises(ValueError, match=msg):
         df.interpolate(method="pad", inplace=True, downcast="infer")
+        assert df._mgr._has_no_reference(0)
+        assert not np.shares_memory(arr_a, get_array(df, "a"))
 
-    assert df._mgr._has_no_reference(0)
-    assert not np.shares_memory(arr_a, get_array(df, "a"))
     tm.assert_frame_equal(df_orig, view)
 
 
diff --git a/pandas/tests/frame/methods/test_interpolate.py b/pandas/tests/frame/methods/test_interpolate.py
index 2ba3bbd3109a2..0a9d059736e6f 100644
--- a/pandas/tests/frame/methods/test_interpolate.py
+++ b/pandas/tests/frame/methods/test_interpolate.py
@@ -129,13 +129,7 @@ def test_interp_bad_method(self):
                 "C": [1, 2, 3, 5],
             }
         )
-        msg = (
-            r"method must be one of \['linear', 'time', 'index', 'values', "
-            r"'nearest', 'zero', 'slinear', 'quadratic', 'cubic', "
-            r"'barycentric', 'krogh', 'spline', 'polynomial', "
-            r"'from_derivatives', 'piecewise_polynomial', 'pchip', 'akima', "
-            r"'cubicspline'\]. Got 'not_a_method' instead."
-        )
+        msg = "Can not interpolate with method=not_a_method"
         with pytest.raises(ValueError, match=msg):
             df.interpolate(method="not_a_method")
 
@@ -398,12 +392,9 @@ def test_interp_fillna_methods(self, axis, multiblock, method):
             df["D"] = np.nan
             df["E"] = 1.0
 
-        method2 = method if method != "pad" else "ffill"
-        expected = getattr(df, method2)(axis=axis)
-        msg = f"DataFrame.interpolate with method={method} is deprecated"
-        with tm.assert_produces_warning(FutureWarning, match=msg):
-            result = df.interpolate(method=method, axis=axis)
-        tm.assert_frame_equal(result, expected)
+        msg = f"Can not interpolate with method={method}"
+        with pytest.raises(ValueError, match=msg):
+            df.interpolate(method=method, axis=axis)
 
     def test_interpolate_empty_df(self):
         # GH#53199
diff --git a/pandas/tests/series/methods/test_interpolate.py b/pandas/tests/series/methods/test_interpolate.py
index e4726f3ec6b32..c5df1fd498938 100644
--- a/pandas/tests/series/methods/test_interpolate.py
+++ b/pandas/tests/series/methods/test_interpolate.py
@@ -344,7 +344,7 @@ def test_interpolate_invalid_float_limit(self, nontemporal_method):
     def test_interp_invalid_method(self, invalid_method):
         s = Series([1, 3, np.nan, 12, np.nan, 25])
 
-        msg = f"method must be one of.* Got '{invalid_method}' instead"
+        msg = "Can not interpolate with method=nonexistent_method"
         if invalid_method is None:
             msg = "'method' should be a string, not None"
         with pytest.raises(ValueError, match=msg):
@@ -355,16 +355,6 @@ def test_interp_invalid_method(self, invalid_method):
         with pytest.raises(ValueError, match=msg):
             s.interpolate(method=invalid_method, limit=-1)
 
-    def test_interp_invalid_method_and_value(self):
-        # GH#36624
-        ser = Series([1, 3, np.nan, 12, np.nan, 25])
-
-        msg = "'fill_value' is not a valid keyword for Series.interpolate"
-        msg2 = "Series.interpolate with method=pad"
-        with pytest.raises(ValueError, match=msg):
-            with tm.assert_produces_warning(FutureWarning, match=msg2):
-                ser.interpolate(fill_value=3, method="pad")
-
     def test_interp_limit_forward(self):
         s = Series([1, 3, np.nan, np.nan, np.nan, 11])
 
@@ -455,107 +445,70 @@ def test_interp_limit_area(self):
             s.interpolate(method="linear", limit_area="abc")
 
     @pytest.mark.parametrize(
-        "method, limit_direction, expected",
-        [
-            ("pad", "backward", "forward"),
-            ("ffill", "backward", "forward"),
-            ("backfill", "forward", "backward"),
-            ("bfill", "forward", "backward"),
-            ("pad", "both", "forward"),
-            ("ffill", "both", "forward"),
-            ("backfill", "both", "backward"),
-            ("bfill", "both", "backward"),
-        ],
-    )
-    def test_interp_limit_direction_raises(self, method, limit_direction, expected):
-        # https://github.com/pandas-dev/pandas/pull/34746
-        s = Series([1, 2, 3])
-
-        msg = f"`limit_direction` must be '{expected}' for method `{method}`"
-        msg2 = "Series.interpolate with method="
-        with pytest.raises(ValueError, match=msg):
-            with tm.assert_produces_warning(FutureWarning, match=msg2):
-                s.interpolate(method=method, limit_direction=limit_direction)
-
-    @pytest.mark.parametrize(
-        "data, expected_data, kwargs",
+        "data, kwargs",
         (
             (
                 [np.nan, np.nan, 3, np.nan, np.nan, np.nan, 7, np.nan, np.nan],
-                [np.nan, np.nan, 3.0, 3.0, 3.0, 3.0, 7.0, np.nan, np.nan],
                 {"method": "pad", "limit_area": "inside"},
             ),
             (
                 [np.nan, np.nan, 3, np.nan, np.nan, np.nan, 7, np.nan, np.nan],
-                [np.nan, np.nan, 3.0, 3.0, np.nan, np.nan, 7.0, np.nan, np.nan],
                 {"method": "pad", "limit_area": "inside", "limit": 1},
             ),
             (
                 [np.nan, np.nan, 3, np.nan, np.nan, np.nan, 7, np.nan, np.nan],
-                [np.nan, np.nan, 3.0, np.nan, np.nan, np.nan, 7.0, 7.0, 7.0],
                 {"method": "pad", "limit_area": "outside"},
             ),
             (
                 [np.nan, np.nan, 3, np.nan, np.nan, np.nan, 7, np.nan, np.nan],
-                [np.nan, np.nan, 3.0, np.nan, np.nan, np.nan, 7.0, 7.0, np.nan],
                 {"method": "pad", "limit_area": "outside", "limit": 1},
             ),
             (
-                [np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan],
                 [np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan],
                 {"method": "pad", "limit_area": "outside", "limit": 1},
             ),
             (
-                range(5),
                 range(5),
                 {"method": "pad", "limit_area": "outside", "limit": 1},
             ),
         ),
     )
-    def test_interp_limit_area_with_pad(self, data, expected_data, kwargs):
+    def test_interp_limit_area_with_pad(self, data, kwargs):
         # GH26796
 
         s = Series(data)
-        expected = Series(expected_data)
-        msg = "Series.interpolate with method=pad"
-        with tm.assert_produces_warning(FutureWarning, match=msg):
-            result = s.interpolate(**kwargs)
-        tm.assert_series_equal(result, expected)
+        msg = "Can not interpolate with method=pad"
+        with pytest.raises(ValueError, match=msg):
+            s.interpolate(**kwargs)
 
     @pytest.mark.parametrize(
-        "data, expected_data, kwargs",
+        "data, kwargs",
         (
             (
                 [np.nan, np.nan, 3, np.nan, np.nan, np.nan, 7, np.nan, np.nan],
-                [np.nan, np.nan, 3.0, 7.0, 7.0, 7.0, 7.0, np.nan, np.nan],
                 {"method": "bfill", "limit_area": "inside"},
             ),
             (
                 [np.nan, np.nan, 3, np.nan, np.nan, np.nan, 7, np.nan, np.nan],
-                [np.nan, np.nan, 3.0, np.nan, np.nan, 7.0, 7.0, np.nan, np.nan],
                 {"method": "bfill", "limit_area": "inside", "limit": 1},
             ),
             (
                 [np.nan, np.nan, 3, np.nan, np.nan, np.nan, 7, np.nan, np.nan],
-                [3.0, 3.0, 3.0, np.nan, np.nan, np.nan, 7.0, np.nan, np.nan],
                 {"method": "bfill", "limit_area": "outside"},
             ),
             (
                 [np.nan, np.nan, 3, np.nan, np.nan, np.nan, 7, np.nan, np.nan],
-                [np.nan, 3.0, 3.0, np.nan, np.nan, np.nan, 7.0, np.nan, np.nan],
                 {"method": "bfill", "limit_area": "outside", "limit": 1},
             ),
         ),
     )
-    def test_interp_limit_area_with_backfill(self, data, expected_data, kwargs):
+    def test_interp_limit_area_with_backfill(self, data, kwargs):
         # GH26796
-
         s = Series(data)
-        expected = Series(expected_data)
-        msg = "Series.interpolate with method=bfill"
-        with tm.assert_produces_warning(FutureWarning, match=msg):
-            result = s.interpolate(**kwargs)
-        tm.assert_series_equal(result, expected)
+
+        msg = "Can not interpolate with method=bfill"
+        with pytest.raises(ValueError, match=msg):
+            s.interpolate(**kwargs)
 
     def test_interp_limit_direction(self):
         # These tests are for issue #9218 -- fill NaNs in both directions.
@@ -650,20 +603,18 @@ def test_interp_datetime64(self, method, tz_naive_fixture):
         df = Series(
             [1, np.nan, 3], index=date_range("1/1/2000", periods=3, tz=tz_naive_fixture)
         )
-        warn = None if method == "nearest" else FutureWarning
-        msg = "Series.interpolate with method=pad is deprecated"
-        with tm.assert_produces_warning(warn, match=msg):
-            result = df.interpolate(method=method)
-        if warn is not None:
-            # check the "use ffill instead" is equivalent
-            alt = df.ffill()
-            tm.assert_series_equal(result, alt)
 
-        expected = Series(
-            [1.0, 1.0, 3.0],
-            index=date_range("1/1/2000", periods=3, tz=tz_naive_fixture),
-        )
-        tm.assert_series_equal(result, expected)
+        if method == "nearest":
+            result = df.interpolate(method=method)
+            expected = Series(
+                [1.0, 1.0, 3.0],
+                index=date_range("1/1/2000", periods=3, tz=tz_naive_fixture),
+            )
+            tm.assert_series_equal(result, expected)
+        else:
+            msg = "Can not interpolate with method=pad"
+            with pytest.raises(ValueError, match=msg):
+                df.interpolate(method=method)
 
     def test_interp_pad_datetime64tz_values(self):
         # GH#27628 missing.interpolate_2d should handle datetimetz values
@@ -671,16 +622,9 @@ def test_interp_pad_datetime64tz_values(self):
         ser = Series(dti)
         ser[1] = pd.NaT
 
-        msg = "Series.interpolate with method=pad is deprecated"
-        with tm.assert_produces_warning(FutureWarning, match=msg):
-            result = ser.interpolate(method="pad")
-        # check the "use ffill instead" is equivalent
-        alt = ser.ffill()
-        tm.assert_series_equal(result, alt)
-
-        expected = Series(dti)
-        expected[1] = expected[0]
-        tm.assert_series_equal(result, expected)
+        msg = "Can not interpolate with method=pad"
+        with pytest.raises(ValueError, match=msg):
+            ser.interpolate(method="pad")
 
     def test_interp_limit_no_nans(self):
         # GH 7173