This article presents a review of selected multiaxial high-cycle fatigue criteria with an emphasis on their ability to take into account the mean stress effect and the effect of a biaxial stress state. It is shown that the predictions of the various criteria are very different for the case of biaxial tensile loads. This is in contrast to the case of combined tension-torsion loads, where the predictions are very similar. The second part of the article investigates which mechanical parameter (eg, the hydrostatic stress or the normal stress) is the most appropriate to take into account these cyclic stress states.