diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 5c74965bffdd7..dd6ca8a0c969a 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -733,6 +733,8 @@ Missing
 - Bug in :meth:`replace` when argument ``to_replace`` is of type dict/list and is used on a :class:`Series` containing ``<NA>`` was raising a ``TypeError``. The method now handles this by ignoring ``<NA>`` values when doing the comparison for the replacement (:issue:`32621`)
 - Bug in :meth:`~Series.any` and :meth:`~Series.all` incorrectly returning ``<NA>`` for all ``False`` or all ``True`` values using the nulllable boolean dtype and with ``skipna=False`` (:issue:`33253`)
 - Clarified documentation on interpolate with method =akima. The ``der`` parameter must be scalar or None (:issue:`33426`)
+- :meth:`DataFrame.interpolate` uses the correct axis convention now. Previously interpolating along columns lead to interpolation along indices and vice versa. Furthermore interpolating with methods ``pad``, ``ffill``, ``bfill`` and ``backfill`` are identical to using these methods with :meth:`fillna` (:issue:`12918`, :issue:`29146`)
+- Bug in :meth:`DataFrame.interpolate` when called on a DataFrame with column names of string type was throwing a ValueError. The method is no independing of the type of column names (:issue:`33956`)
 
 MultiIndex
 ^^^^^^^^^^
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 85b6a8431617a..e9f7bf457cbfd 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -6881,30 +6881,42 @@ def interpolate(
         inplace = validate_bool_kwarg(inplace, "inplace")
 
         axis = self._get_axis_number(axis)
+        index = self._get_axis(axis)
+
+        if isinstance(self.index, MultiIndex) and method != "linear":
+            raise ValueError(
+                "Only `method=linear` interpolation is supported on MultiIndexes."
+            )
+
+        # for the methods backfill, bfill, pad, ffill limit_direction and limit_area
+        # are being ignored, see gh-26796 for more information
+        if method in ["backfill", "bfill", "pad", "ffill"]:
+            return self.fillna(
+                method=method,
+                axis=axis,
+                inplace=inplace,
+                limit=limit,
+                downcast=downcast,
+            )
 
+        # Currently we need this to call the axis correctly inside the various
+        # interpolation methods
         if axis == 0:
             df = self
         else:
             df = self.T
 
-        if isinstance(df.index, MultiIndex) and method != "linear":
-            raise ValueError(
-                "Only `method=linear` interpolation is supported on MultiIndexes."
-            )
-
-        if df.ndim == 2 and np.all(df.dtypes == np.dtype(object)):
+        if self.ndim == 2 and np.all(self.dtypes == np.dtype(object)):
             raise TypeError(
                 "Cannot interpolate with all object-dtype columns "
                 "in the DataFrame. Try setting at least one "
                 "column to a numeric dtype."
             )
 
-        # create/use the index
         if method == "linear":
             # prior default
             index = np.arange(len(df.index))
         else:
-            index = df.index
             methods = {"index", "values", "nearest", "time"}
             is_numeric_or_datetime = (
                 is_numeric_dtype(index.dtype)
diff --git a/pandas/tests/frame/methods/test_interpolate.py b/pandas/tests/frame/methods/test_interpolate.py
index 291a46cf03216..efb3d719016bb 100644
--- a/pandas/tests/frame/methods/test_interpolate.py
+++ b/pandas/tests/frame/methods/test_interpolate.py
@@ -202,7 +202,7 @@ def test_interp_leading_nans(self, check_scipy):
             result = df.interpolate(method="polynomial", order=1)
             tm.assert_frame_equal(result, expected)
 
-    def test_interp_raise_on_only_mixed(self):
+    def test_interp_raise_on_only_mixed(self, axis):
         df = DataFrame(
             {
                 "A": [1, 2, np.nan, 4],
@@ -212,8 +212,13 @@ def test_interp_raise_on_only_mixed(self):
                 "E": [1, 2, 3, 4],
             }
         )
-        with pytest.raises(TypeError):
-            df.interpolate(axis=1)
+        msg = (
+            "Cannot interpolate with all object-dtype columns "
+            "in the DataFrame. Try setting at least one "
+            "column to a numeric dtype."
+        )
+        with pytest.raises(TypeError, match=msg):
+            df.astype("object").interpolate(axis=axis)
 
     def test_interp_raise_on_all_object_dtype(self):
         # GH 22985
@@ -272,7 +277,6 @@ def test_interp_ignore_all_good(self):
         result = df[["B", "D"]].interpolate(downcast=None)
         tm.assert_frame_equal(result, df[["B", "D"]])
 
-    @pytest.mark.parametrize("axis", [0, 1])
     def test_interp_time_inplace_axis(self, axis):
         # GH 9687
         periods = 5
@@ -296,3 +300,17 @@ def test_interp_string_axis(self, axis_name, axis_number):
         result = df.interpolate(method="linear", axis=axis_name)
         expected = df.interpolate(method="linear", axis=axis_number)
         tm.assert_frame_equal(result, expected)
+
+    @pytest.mark.parametrize("method", ["ffill", "bfill", "pad"])
+    def test_interp_fillna_methods(self, axis, method):
+        # GH 12918
+        df = DataFrame(
+            {
+                "A": [1.0, 2.0, 3.0, 4.0, np.nan, 5.0],
+                "B": [2.0, 4.0, 6.0, np.nan, 8.0, 10.0],
+                "C": [3.0, 6.0, 9.0, np.nan, np.nan, 30.0],
+            }
+        )
+        expected = df.fillna(axis=axis, method=method)
+        result = df.interpolate(method=method, axis=axis)
+        tm.assert_frame_equal(result, expected)