Binocular rivalry (BR) occurs when the brain cannot fuse percepts from the two eyes because they are different. We review results relating to an ongoing controversy regarding the cortical site of the BR mechanism. Some BR qualities suggest it is low-level: (1) BR, as its name implies, is usually between eyes and only low-levels have access to utrocular information. (2) All input to one eye is suppressed: blurring doesn’t stimulate accommodation; pupilary constrictions are reduced; probe detection is reduced. (3) Rivalry is affected by low-level attributes, contrast, spatial frequency, brightness, motion. (4) There is limited priming due to suppressed words or pictures. On the other hand, recent studies favor a high-level mechanism: (1) Rivalry occurs between patterns, not eyes, as in patchwork rivalry or a swapping paradigm. (2) Attention affects alternations. (3) Context affects dominance. There is conflicting evidence from physiological studies (single cell and fMRI) regarding cortical level(s) of conscious perception. We discuss the possibility of multiple BR sites and theoretical considerations that rule out this solution. We present new data regarding the locus of the BR switch by manipulating stimulus semantic content or high-level characteristics. Since these variations are represented at higher cortical levels, their affecting rivalry supports high-level BR intervention. In Experiment I, we measure rivalry when one eye views words and the other non-words and find significantly longer dominance durations for non-words. In Experiment II, we find longer dominance times for line drawings of simple, structurally impossible figures than for similar, possible objects. In Experiment III, we test the influence of idiomatic context on rivalry between words. Results show that generally words within their idiomatic context have longer mean dominance durations. We conclude that BR has high-level cortical influences, and may be controlled by a high-level mechanism.