During binocular rivalry, conflicting monocular images compete for access to consciousness in a stochastic, dynamical fashion. Recent human neuroimaging and psychophysical studies suggest that rivalry entails competitive interactions at multiple neural sites, including sites that retain eye-selective information. Rivalry greatly suppresses activity in the ventral pathway and attenuates visual adaptation to form and motion; nonetheless, some information about the suppressed stimulus reaches higher brain areas. Although rivalry depends on low-level inhibitory interactions, high-level excitatory influences promoting perceptual grouping and selective attention can extend the local dominance of a stimulus over space and time. Inhibitory and excitatory circuits considered within a hybrid model might account for the paradoxical properties of binocular rivalry and provide insights into the neural bases of visual awareness itself.