diff --git a/ibis_ml/steps/_impute.py b/ibis_ml/steps/_impute.py
index 1436cab..7d0bfbf 100644
--- a/ibis_ml/steps/_impute.py
+++ b/ibis_ml/steps/_impute.py
@@ -1,5 +1,6 @@
 from __future__ import annotations
 
+import math
 from typing import TYPE_CHECKING, Any
 
 import ibis.expr.types as ir
@@ -14,6 +15,8 @@
 
 
 def _fillna(col, val):
+    if val is None or col.type().is_floating() and math.isnan(val):
+        raise ValueError(f"Cannot fill column {col.get_name()!r} with `None` or `NaN`")
     if col.type().is_floating():
         return (col.isnull() | col.isnan()).ifelse(val, col)  # noqa: PD003
     else:
diff --git a/tests/test_impute.py b/tests/test_impute.py
new file mode 100644
index 0000000..8ec7e62
--- /dev/null
+++ b/tests/test_impute.py
@@ -0,0 +1,56 @@
+import ibis
+import numpy as np
+import pandas as pd
+import pandas.testing as tm
+import pytest
+
+import ibis_ml as ml
+
+
+@pytest.mark.parametrize(
+    ("mode", "col_name", "expected"),
+    [
+        ("mean", "floating_col", 1.0),
+        ("median", "floating_col", 0.0),
+        ("mode", "floating_col", 0.0),
+        ("mean", "int_col", 1),
+        ("median", "int_col", 0),
+        ("mode", "int_col", 0),
+        ("mode", "string_col", "a"),
+    ]
+)
+def test_impute(mode, col_name, expected):
+    mode_class = getattr(ml, f"Impute{mode.capitalize()}")
+    step = mode_class(col_name)
+    train_table = ibis.memtable(
+        {
+            "floating_col": [0.0, 0.0, 3.0, None, np.nan],
+            "int_col": [0, 0, 3, None, None],
+            "string_col": ["a", "a", "c", None, None],
+            "null_col": [None]*5,
+        }
+    )
+    test_table = ibis.memtable(
+        {
+            col_name: [None],
+        }
+    )
+    step.fit_table(train_table, ml.core.Metadata())
+    result = step.transform_table(test_table)
+    expected = pd.DataFrame(
+        {
+            col_name: [expected],
+        }
+    )
+    tm.assert_frame_equal(result.execute(), expected, check_dtype=False)
+
+    # null col will raise a ValueError
+    test_table = ibis.memtable(
+        {
+            "null_col": [None],
+        }
+    )
+    with pytest.raises(ValueError):
+        step = mode_class("null_col")
+        step.fit_table(train_table, ml.core.Metadata())
+        step.transform_table(test_table)
\ No newline at end of file