Figures that can be seen in more than one way are invaluable tools for the study of the neural basis of visual awareness, because such stimuli permit the dissociation of the neural responses that underlie what we perceive at any given time from those forming the sensory representation of a visual pattern. To study the former type of responses, monkeys were subjected to binocular rivalry, and the response of neurons in a number of different visual areas was studied while the animals reported their alternating percepts by pulling levers. Perception–related modulations of neural activity were found to occur to different extents in different cortical visual areas. The cells that were affected by suppression were almost exclusively binocular, and their proportion was found to increase in the higher processing stages of the visual system. The strongest correlations between neural activity and perception were observed in the visual areas of the temporal lobe. A strikingly large number of neurons in the early visual areas remained active during the perceptual suppression of the stimulus, a finding suggesting that conscious visual perception might be mediated by only a subset of the cells exhibiting stimulus selective responses. These physiological findings, together with a number of recent psychophysical studies, offer a new explanation of the phenomenon of binocular rivalry. Indeed, rivalry has long been considered to be closely linked with binocular fusion and stereopsis, and the sequences of dominance and suppression have been viewed as the result of competition between the two monocular channels. The physiological data presented here are incompatible with this interpretation. Rather than reflecting interocular competition, the rivalry is most probably between the two different central neural representations generated by the dichoptically presented stimuli. The mechanisms of rivalry are probably the same as, or very similar to, those underlying multistable perception in general, and further physiological studies might reveal a much about the neural mechanisms of our perceptual organization.