Visual masking effects are illusions in which a target is rendered invisible by a mask, which can either overlap or not overlap the target spatially and/or temporally. These illusions provide a powerful tool to study visibility and consciousness, object grouping, brightness perception, and much more. As such, the physiological mechanisms underlying the perception of masking are critically important to our understanding of visibility. Several models that require cortical circuits have been proposed previously to explain the mysterious spatial and timing effects associated with visual masking. Here we describe single-unit physiological experiments from the awake monkey that show that visual masking occurs in at least two separate and independent circuits, one that is binocular and one that is monocular (possibly even subcortical), without feedback from higher-level visual brain areas. These and other results together fail to support models of masking that require circuits found only in the cortex, but support our proposed model that suggests that simple ubiquitous lateral inhibition may itself be the fundamental mechanism that explains visual masking across multiple levels in the brain. We also show that area V1 neurons are dichoptic in terms of excitation, but monoptic in terms of inhibition. That is, responses within area V1 binocular neurons reveal that excitation to monocular targets is inhibited strongly only by masks presented to the same eye, and not by masks presented to the opposite eye. These results lead us to redefine the model for the first stage of binocular processing in the visual system, and may be crucial to interpreting the effects of other similar binocular and dichoptic stimulation paradigms, such as the binocular rivalry family of illusions.