Substantial experimental, theoretical, and computational insights into sensory processing have been derived from the phenomena of perceptual multistability—when two or more percepts alternate or switch in response to a single sensory input. Here, we review a range of findings suggesting that alternations can be seen as internal choices by the brain responding to values. We discuss how elements of external, experimenter-controlled values and internal, uncertainty- and aesthetics-dependent values influence multistability. We then consider the implications for the involvement in switching of regions, such as the anterior cingulate cortex, which are more conventionally tied to value-dependent operations such as cognitive control and foraging.