Pictures that spontaneously change in appearance, such as depth or figure-ground reversals, have always been thought of as powerful tools for understaning the nature of the perceptual system. The cause of the perceptual multistability that is experienced when viewing such figures most likely lies in the brain's physical organization; an organization that imposes several constraints on the processing of visual information. Why is it that our visual system fails to lock onto one aspect of an ambiguous figure? What accounts for the spontaneous changes of interpretation? What are the neural events that underlie such changes? Are there neurons in the visual pathways the activity of which reflects the visual awareness of the stimulus? In my paper I describe some combined psychophysical and physiological experiments that were motivated by these questions. In specific, we report on experiments in which neural activity in early visual cortex and in the inferior temporal cortex of monkeys was studied, while the animals experienced binocular rivalry. Our results provide us with new evidence not only on the neural mechanisms of binocular rivalry (one example of multistable perception), but also on the neural processes underlying image segmentation and perceptual grouping.