diff --git a/feature_engine/dataframe_checks.py b/feature_engine/dataframe_checks.py
index ae3be3c7b..b3a07be12 100644
--- a/feature_engine/dataframe_checks.py
+++ b/feature_engine/dataframe_checks.py
@@ -2,23 +2,27 @@
 transform().
 """
 
-from typing import List, Union
+from typing import List, Tuple, Union
 
 import narwhals as nw
 import narwhals.dependencies as nwd
+import narwhals.selectors as nws
 import numpy as np
-from narwhals.typing import IntoDataFrame, IntoSeries
+from narwhals.typing import IntoDataFrame, IntoDataFrameT, IntoSeries
 from sklearn.utils.validation import _check_y, check_consistent_length, column_or_1d
 
 
-def check_X(X: IntoDataFrame):
+def check_X(X: IntoDataFrameT) -> IntoDataFrameT:
     """
     Checks that X is a dataframe from any library supported by narwhals (for example
     pandas, polars, modin, cuDF, or PyArrow).
 
     Parameters
     ----------
-    X : dataframe (pandas, polars, or any other library supported by narwhals).
+    X : dataframe (pandas, polars, PyArrow, modin, or cuDF). Feature-engine does
+        not support libraries that build a deferred query plan (for example Dask,
+        DuckDB, PySpark, Ibis, or a polars LazyFrame). Convert those to an eager
+        dataframe (e.g. `LazyFrame.collect()`) before passing them in.
         The input to check and transform.
 
     Raises
@@ -63,8 +67,11 @@ def check_y(
 
     Parameters
     ----------
-    y : Series or DataFrame (pandas, polars, or any other library supported by
-        narwhals), np.array, list
+    y : Series or DataFrame (pandas, polars, PyArrow, modin, or cuDF), np.array,
+        list. Feature-engine does not support libraries that build a deferred
+        query plan (for example Dask, DuckDB, PySpark, Ibis, or a polars
+        LazyFrame). Convert those to an eager dataframe (e.g. `LazyFrame.collect()`)
+        before passing them in.
         The input to check.
 
     y_numeric : bool, default=False
@@ -84,7 +91,9 @@ def check_y(
 
     if nwd.is_into_series(y):
         nw_y = nw.from_native(y, series_only=True)
-        if nw_y.is_null().any():
+        if nw_y.is_null().any() or (
+            nw_y.dtype.is_numeric() and nw_y.is_nan().any()
+        ):
             raise ValueError("y contains NaN values.")
         if nw_y.dtype.is_numeric():
             if not np.isfinite(nw_y.to_numpy()).all():
@@ -95,7 +104,10 @@ def check_y(
 
     if nwd.is_into_dataframe(y):
         nw_y = nw.from_native(y, eager_only=True)
-        if nw_y.select(nw.all().is_null().any()).to_numpy().any():
+        if (
+            nw_y.select(nw.all().is_null().any()).to_numpy().any()
+            or nw_y.select(nws.numeric().is_nan().any()).to_numpy().any()
+        ):
             raise ValueError("y contains NaN values.")
         if not np.isfinite(nw_y.to_numpy()).all():
             raise ValueError("y contains infinity values.")
@@ -109,17 +121,20 @@ def check_y(
 
 
 def check_X_y(
-    X: IntoDataFrame,
+    X: IntoDataFrameT,
     y: Union[IntoSeries, IntoDataFrame, np.generic, np.ndarray, List],
     y_numeric: bool = False,
-):
+) -> Tuple[IntoDataFrameT, Union[IntoSeries, IntoDataFrame, np.ndarray]]:
     """
     Ensures X and y are compatible dataframe/array-like objects with a consistent
     number of rows. If both are pandas objects, checks that their indexes match.
 
     Parameters
     ----------
-    X: dataframe (pandas, polars, or any other library supported by narwhals)
+    X: dataframe (pandas, polars, PyArrow, modin, or cuDF). Feature-engine does
+        not support libraries that build a deferred query plan (for example Dask,
+        DuckDB, PySpark, Ibis, or a polars LazyFrame). Convert those to an eager
+        dataframe (e.g. `LazyFrame.collect()`) before passing them in.
         The input to check.
 
     y: Series, DataFrame (pandas, polars, or any other library supported by
@@ -213,7 +228,14 @@ def _check_contains_na(
         "`missing_values='ignore'` when initialising this transformer."
     )
     nw_X = nw.from_native(X, eager_only=True)
-    if nw_X.select(nw.col(variables).is_null().any()).to_numpy().any():
+    if nwd.is_pandas_dataframe(X):
+        numeric_vars = list(X[variables].select_dtypes(include="number").columns)
+    else:
+        numeric_vars = nw_X.select(variables).select(nw.selectors.numeric()).columns
+    if nw_X.select(nw.col(variables).is_null().any()).to_numpy().any() or (
+        numeric_vars
+        and nw_X.select(nw.col(numeric_vars).is_nan().any()).to_numpy().any()
+    ):
         if error_msg == "simple":
             raise ValueError(error_msg_simple)
         else:
diff --git a/tests/test_dataframe_checks.py b/tests/test_dataframe_checks.py
index 085a82fad..ccef69112 100644
--- a/tests/test_dataframe_checks.py
+++ b/tests/test_dataframe_checks.py
@@ -132,6 +132,18 @@ def test_check_y_series_raises_nan_error(make_series):
         check_y(s)
 
 
+@pytest.mark.parametrize(
+    "make_series",
+    [pd.Series, pl.Series],
+)
+def test_check_y_series_raises_nan_error_for_explicit_nan(make_series):
+    # in polars, an explicit float("nan") is not a null value, so it is only
+    # caught if is_nan() is checked in addition to is_null()
+    s = make_series([0.0, float("nan"), 2.0])
+    with pytest.raises(ValueError, match="y contains NaN values."):
+        check_y(s)
+
+
 @pytest.mark.parametrize(
     "make_series",
     [pd.Series, pl.Series],
@@ -190,6 +202,18 @@ def test_check_y_dataframe_raises_nan_error(make_df):
         check_y(d)
 
 
+@pytest.mark.parametrize(
+    "make_df",
+    [pd.DataFrame, pl.DataFrame],
+)
+def test_check_y_dataframe_raises_nan_error_for_explicit_nan(make_df):
+    # in polars, an explicit float("nan") is not a null value, so it is only
+    # caught if is_nan() is checked in addition to is_null()
+    d = make_df({"t1": [0.0, float("nan"), 2.0], "t2": [5.0, 6.0, 7.0]})
+    with pytest.raises(ValueError, match="y contains NaN values."):
+        check_y(d)
+
+
 @pytest.mark.parametrize(
     "make_df",
     [pd.DataFrame, pl.DataFrame],
@@ -372,6 +396,33 @@ def test_contains_na_ignores_columns_not_in_variables(make_df):
     assert _check_contains_na(df, ["City"]) is None
 
 
+@pytest.mark.parametrize("make_df", [pd.DataFrame, pl.DataFrame])
+def test_contains_na_raises_for_explicit_nan_in_numeric_column(make_df):
+    # in polars, an explicit float("nan") is not a null value, so it is only
+    # caught if is_nan() is checked in addition to is_null()
+    msg = (
+        "Some of the variables in the dataset contain NaN. Check and "
+        "remove those before using this transformer."
+    )
+    df = make_df({"Age": [20.0, float("nan"), 19.0], "City": ["a", "b", "c"]})
+    with pytest.raises(ValueError, match=msg):
+        _check_contains_na(df, ["Age", "City"])
+
+
+@pytest.mark.parametrize("make_df", [pd.DataFrame, pl.DataFrame])
+def test_contains_na_raises_for_mix_of_null_and_nan_across_dtypes(make_df):
+    # a numeric column with a NaN and a string column with a null should both
+    # still be caught, and the numeric-only is_nan() scoping must not error out
+    # on the string column
+    msg = (
+        "Some of the variables in the dataset contain NaN. Check and "
+        "remove those before using this transformer."
+    )
+    df = make_df({"Age": [20.0, float("nan"), 19.0], "City": ["a", None, "c"]})
+    with pytest.raises(ValueError, match=msg):
+        _check_contains_na(df, ["Age", "City"])
+
+
 # --------------------------
 # test _check_contains_inf
 # --------------------------