The ability to mentally represent the movement of hidden objects (i.e., invisible displacement) is of theoretical importance due to its generally accepted status as an indicator of the development of a powerful type of representational capacity in human children. Over the past few decades, the understanding of invisible displacement has been claimed for a variety of animal species as well. However, a careful review of these studies finds that: (a) many were not properly blinded, (b) many did not properly control for lower-level associative strategies, and (c) success on simplified versions of the tasks can be explained by a simple attentional mechanism rather than by conceptual understanding. Indeed, when lower-level factors are controlled, evidence of understanding invisible displacement remains only for great apes.