diff --git a/src/probnum/quad/_bayesquad.py b/src/probnum/quad/_bayesquad.py
index c888fcbfc..73787e980 100644
--- a/src/probnum/quad/_bayesquad.py
+++ b/src/probnum/quad/_bayesquad.py
@@ -156,6 +156,12 @@ def bayesquad(
     bayesquad_from_data : Computes the integral :math:`F` using a given dataset of
                           nodes and function evaluations.
 
+    Warnings
+    --------
+    Currently the method does not support tuning of the kernel parameters
+    other than the global kernel scale. Hence, the method may perform poorly unless the
+    kernel parameters are set to appropriate values by the user.
+
     References
     ----------
     .. [1] Briol, F.-X., et al., Probabilistic integration: A role in statistical
@@ -260,6 +266,12 @@ def bayesquad_from_data(
     --------
     bayesquad : Computes the integral using an acquisition policy.
 
+    Warnings
+    --------
+    Currently the method does not support tuning of the kernel parameters
+    other than the global kernel scale. Hence, the method may perform poorly unless the
+    kernel parameters are set to appropriate values by the user.
+
     Examples
     --------
     >>> import numpy as np
@@ -383,6 +395,12 @@ def multilevel_bayesquad_from_data(
     kernel instances, i.e., ``kernels[i] is kernel[j]`` must return ``False`` for any
     :math:`i\neq j`.
 
+    Warnings
+    --------
+    Currently the method does not support tuning of the kernel parameters
+    other than the global kernel scale. Hence, the method may perform poorly unless the
+    kernel parameters are set to appropriate values by the user.
+
     References
     ----------
     .. [1] Li, K., et al., Multilevel Bayesian quadrature, AISTATS, 2023.