diff --git a/xarray/core/rolling_exp.py b/xarray/core/rolling_exp.py
index 4935f3c8172..f3a9aed42c6 100644
--- a/xarray/core/rolling_exp.py
+++ b/xarray/core/rolling_exp.py
@@ -194,3 +194,133 @@ def sum(self, keep_attrs: bool | None = None) -> T_DataWithCoords:
             on_missing_core_dim="copy",
             dask="parallelized",
         ).transpose(*dim_order)
+
+    def std(self) -> T_DataWithCoords:
+        """
+        Exponentially weighted moving standard deviation.
+
+        `keep_attrs` is always True for this method. Drop attrs separately to remove attrs.
+
+        Examples
+        --------
+        >>> da = xr.DataArray([1, 1, 2, 2, 2], dims="x")
+        >>> da.rolling_exp(x=2, window_type="span").std()
+        <xarray.DataArray (x: 5)>
+        array([       nan, 0.        , 0.67936622, 0.42966892, 0.25389527])
+        Dimensions without coordinates: x
+        """
+
+        if has_numbagg is False or has_numbagg < "0.4.0":
+            raise ImportError(
+                f"numbagg >= 0.4.0 is required for rolling_exp().std(), currently {has_numbagg} is installed"
+            )
+        dim_order = self.obj.dims
+
+        return apply_ufunc(
+            numbagg.move_exp_nanstd,
+            self.obj,
+            input_core_dims=[[self.dim]],
+            kwargs=self.kwargs,
+            output_core_dims=[[self.dim]],
+            keep_attrs=True,
+            on_missing_core_dim="copy",
+            dask="parallelized",
+        ).transpose(*dim_order)
+
+    def var(self) -> T_DataWithCoords:
+        """
+        Exponentially weighted moving variance.
+
+        `keep_attrs` is always True for this method. Drop attrs separately to remove attrs.
+
+        Examples
+        --------
+        >>> da = xr.DataArray([1, 1, 2, 2, 2], dims="x")
+        >>> da.rolling_exp(x=2, window_type="span").var()
+        <xarray.DataArray (x: 5)>
+        array([       nan, 0.        , 0.46153846, 0.18461538, 0.06446281])
+        Dimensions without coordinates: x
+        """
+
+        if has_numbagg is False or has_numbagg < "0.4.0":
+            raise ImportError(
+                f"numbagg >= 0.4.0 is required for rolling_exp().var(), currently {has_numbagg} is installed"
+            )
+        dim_order = self.obj.dims
+
+        return apply_ufunc(
+            numbagg.move_exp_nanvar,
+            self.obj,
+            input_core_dims=[[self.dim]],
+            kwargs=self.kwargs,
+            output_core_dims=[[self.dim]],
+            keep_attrs=True,
+            on_missing_core_dim="copy",
+            dask="parallelized",
+        ).transpose(*dim_order)
+
+    def cov(self, other: T_DataWithCoords) -> T_DataWithCoords:
+        """
+        Exponentially weighted moving covariance.
+
+        `keep_attrs` is always True for this method. Drop attrs separately to remove attrs.
+
+        Examples
+        --------
+        >>> da = xr.DataArray([1, 1, 2, 2, 2], dims="x")
+        >>> da.rolling_exp(x=2, window_type="span").cov(da**2)
+        <xarray.DataArray (x: 5)>
+        array([       nan, 0.        , 1.38461538, 0.55384615, 0.19338843])
+        Dimensions without coordinates: x
+        """
+
+        if has_numbagg is False or has_numbagg < "0.4.0":
+            raise ImportError(
+                f"numbagg >= 0.4.0 is required for rolling_exp().cov(), currently {has_numbagg} is installed"
+            )
+        dim_order = self.obj.dims
+
+        return apply_ufunc(
+            numbagg.move_exp_nancov,
+            self.obj,
+            other,
+            input_core_dims=[[self.dim], [self.dim]],
+            kwargs=self.kwargs,
+            output_core_dims=[[self.dim]],
+            keep_attrs=True,
+            on_missing_core_dim="copy",
+            dask="parallelized",
+        ).transpose(*dim_order)
+
+    def corr(self, other: T_DataWithCoords) -> T_DataWithCoords:
+        """
+        Exponentially weighted moving correlation.
+
+        `keep_attrs` is always True for this method. Drop attrs separately to remove attrs.
+
+        Examples
+        --------
+        >>> da = xr.DataArray([1, 1, 2, 2, 2], dims="x")
+        >>> da.rolling_exp(x=2, window_type="span").corr(da.shift(x=1))
+        <xarray.DataArray (x: 5)>
+        array([       nan,        nan,        nan, 0.4330127 , 0.48038446])
+        Dimensions without coordinates: x
+        """
+
+        if has_numbagg is False or has_numbagg < "0.4.0":
+            raise ImportError(
+                f"numbagg >= 0.4.0 is required for rolling_exp().cov(), currently {has_numbagg} is installed"
+            )
+        dim_order = self.obj.dims
+
+        return apply_ufunc(
+            numbagg.move_exp_nancorr,
+            self.obj,
+            other,
+            input_core_dims=[[self.dim], [self.dim]],
+            kwargs=self.kwargs,
+            output_core_dims=[[self.dim]],
+            keep_attrs=True,
+            on_missing_core_dim="copy",
+            dask="parallelized",
+        ).transpose(*dim_order)
diff --git a/xarray/tests/test_rolling.py b/xarray/tests/test_rolling.py
index da834b76124..3b213db0b88 100644
--- a/xarray/tests/test_rolling.py
+++ b/xarray/tests/test_rolling.py
@@ -394,7 +394,7 @@ class TestDataArrayRollingExp:
         [["span", 5], ["alpha", 0.5], ["com", 0.5], ["halflife", 5]],
     )
     @pytest.mark.parametrize("backend", ["numpy"], indirect=True)
-    @pytest.mark.parametrize("func", ["mean", "sum"])
+    @pytest.mark.parametrize("func", ["mean", "sum", "var", "std"])
     def test_rolling_exp_runs(self, da, dim, window_type, window, func) -> None:
         da = da.where(da > 0.2)