When the two eyes view very dissimilar images, the visual system often fails to combine the images and one experiences stochastically alternating percepts. This phenomenon, called binocular rivalry, has fascinated researchers for centuries since it provides insights into two critical aspects of visual perception: visual consciousness and cortical suppression. Here, we review the mechanisms of binocular rivalry from a cognitive neuroscience perspective, focusing on empirical findings from two widely used methods—functional magnetic resonance imaging (fMRI) and electroencephalography (EEG). With these techniques, researchers have been able to identify the cortical sites of suppression in binocular rivalry, probe neural responses evoked by unconscious (invisible) visual stimuli, and examine the role of top-down attentional signals in rivalry. We conclude by proposing some future directions for the study of binocular rivalry.