diff --git a/doc/source/whatsnew/v1.0.0.rst b/doc/source/whatsnew/v1.0.0.rst
index a6ba7770dadcc..510e19c2f3ef0 100755
--- a/doc/source/whatsnew/v1.0.0.rst
+++ b/doc/source/whatsnew/v1.0.0.rst
@@ -848,6 +848,7 @@ Plotting
 - :func:`set_option` now validates that the plot backend provided to ``'plotting.backend'`` implements the backend when the option is set, rather than when a plot is created (:issue:`28163`)
 - :meth:`DataFrame.plot` now allow a ``backend`` keyword argument to allow changing between backends in one session (:issue:`28619`).
 - Bug in color validation incorrectly raising for non-color styles (:issue:`29122`).
+- Allow :meth: `DataFrame.plot.scatter` to plot ``objects`` and ``datetime`` type data (:issue:`18755`, :issue:`30391`)
 - Bug in :meth:`DataFrame.hist`, ``xrot=0`` does not work with ``by`` and subplots (:issue:`30288`).
 
 Groupby/resample/rolling
diff --git a/pandas/plotting/_matplotlib/core.py b/pandas/plotting/_matplotlib/core.py
index 6da13f188357c..609da140a3f0b 100644
--- a/pandas/plotting/_matplotlib/core.py
+++ b/pandas/plotting/_matplotlib/core.py
@@ -395,6 +395,10 @@ def _compute_plot_data(self):
             include_type = [np.number]
             exclude_type = ["timedelta"]
 
+        # GH 18755, include object and category type for scatter plot
+        if self._kind == "scatter":
+            include_type.extend(["object", "category"])
+
         numeric_data = data.select_dtypes(include=include_type, exclude=exclude_type)
 
         try:
@@ -866,10 +870,13 @@ def __init__(self, data, x, y, **kwargs):
             x = self.data.columns[x]
         if is_integer(y) and not self.data.columns.holds_integer():
             y = self.data.columns[y]
-        if len(self.data[x]._get_numeric_data()) == 0:
-            raise ValueError(self._kind + " requires x column to be numeric")
-        if len(self.data[y]._get_numeric_data()) == 0:
-            raise ValueError(self._kind + " requires y column to be numeric")
+
+        # Scatter plot allows to plot objects data
+        if self._kind == "hexbin":
+            if len(self.data[x]._get_numeric_data()) == 0:
+                raise ValueError(self._kind + " requires x column to be numeric")
+            if len(self.data[y]._get_numeric_data()) == 0:
+                raise ValueError(self._kind + " requires y column to be numeric")
 
         self.x = x
         self.y = y
diff --git a/pandas/tests/plotting/test_frame.py b/pandas/tests/plotting/test_frame.py
index 4fcdc350bc90a..a9ab9d84dbc2f 100644
--- a/pandas/tests/plotting/test_frame.py
+++ b/pandas/tests/plotting/test_frame.py
@@ -1162,6 +1162,27 @@ def test_plot_scatter(self):
         axes = df.plot(x="x", y="y", kind="scatter", subplots=True)
         self._check_axes_shape(axes, axes_num=1, layout=(1, 1))
 
+    def test_scatterplot_datetime_data(self):
+        # GH 30391
+        dates = pd.date_range(start=date(2019, 1, 1), periods=12, freq="W")
+        vals = np.random.normal(0, 1, len(dates))
+        df = pd.DataFrame({"dates": dates, "vals": vals})
+
+        _check_plot_works(df.plot.scatter, x="dates", y="vals")
+        _check_plot_works(df.plot.scatter, x=0, y=1)
+
+    def test_scatterplot_object_data(self):
+        # GH 18755
+        df = pd.DataFrame(dict(a=["A", "B", "C"], b=[2, 3, 4]))
+
+        _check_plot_works(df.plot.scatter, x="a", y="b")
+        _check_plot_works(df.plot.scatter, x=0, y=1)
+
+        df = pd.DataFrame(dict(a=["A", "B", "C"], b=["a", "b", "c"]))
+
+        _check_plot_works(df.plot.scatter, x="a", y="b")
+        _check_plot_works(df.plot.scatter, x=0, y=1)
+
     @pytest.mark.slow
     def test_if_scatterplot_colorbar_affects_xaxis_visibility(self):
         # addressing issue #10611, to ensure colobar does not
@@ -1216,24 +1237,15 @@ def test_if_scatterplot_colorbars_are_next_to_parent_axes(self):
         colorbar_distance = axes_x_coords[3, :] - axes_x_coords[2, :]
         assert np.isclose(parent_distance, colorbar_distance, atol=1e-7).all()
 
+    @pytest.mark.parametrize("x, y", [("x", "y"), ("y", "x"), ("y", "y")])
     @pytest.mark.slow
-    def test_plot_scatter_with_categorical_data(self):
-        # GH 16199
+    def test_plot_scatter_with_categorical_data(self, x, y):
+        # after fixing GH 18755, should be able to plot categorical data
         df = pd.DataFrame(
             {"x": [1, 2, 3, 4], "y": pd.Categorical(["a", "b", "a", "c"])}
         )
 
-        with pytest.raises(ValueError) as ve:
-            df.plot(x="x", y="y", kind="scatter")
-        ve.match("requires y column to be numeric")
-
-        with pytest.raises(ValueError) as ve:
-            df.plot(x="y", y="x", kind="scatter")
-        ve.match("requires x column to be numeric")
-
-        with pytest.raises(ValueError) as ve:
-            df.plot(x="y", y="y", kind="scatter")
-        ve.match("requires x column to be numeric")
+        _check_plot_works(df.plot.scatter, x=x, y=y)
 
     @pytest.mark.slow
     def test_plot_scatter_with_c(self):