Multistable perception is the spontaneous alternation between two or more perceptual states that occurs when sensory information is ambiguous. Multistable phenomena permit dissociation of neural activity related to conscious perception from that related to sensory stimulation, and therefore have been used extensively to study the neural correlates of consciousness. Here, we review recent work on the neural mechanisms underlying multistable perception and how such work has contributed to understanding the neural correlates of consciousness. Particular emphasis is put on the role of high-level brain mechanisms that are involved in actively selecting and interpreting sensory information, and their interactions with lower-level processes that are more directly concerned with the processing of sensory stimulus properties.