Visual sensitivity, probed through perceptual detectability of sudden stimulus onsets, is strongly impaired around the time of saccades. This robust perceptual phenomenon exhibits intriguing stimulus selectivity properties, which have previously been interpreted as reflecting active suppressive signals directly derived from the eye movement commands. However, the neural mechanisms underlying these selective properties have remained elusive. In my talk, I will describe neurophysiological and behavioral experiments that strongly recast interpretations of perceptual saccadic suppression mechanisms. First, using neurophysiology in awake monkeys, and their concomitant behavior, I will describe how different cell types within the same sensory-motor structure can actually exhibit differential forms of saccade-induced suppression. Thus, some neuron types violate the selective properties of perceptual suppression that are so robust in humans. I will then move to identifying a retinal origin of perceptual saccadic suppression, using ex-vivo retinal ganglion cell neurophysiology. Remarkably, the visual dependencies of retinal suppression (in ex-vivo mouse and pig retinae) are the same as the perceptual dependencies reported by human observers seeing similar image sequences, with or without eye movements. I will finally end by showing how this insight, of a visual origin of perceptual saccadic suppression, allows demonstrating that the classic stimulus selective properties of suppression can be easily violated with simple visual manipulations, thus potentially explaining the earlier monkey results alluded to above. This line of work demonstrates that perceptual saccadic suppression may not be saccadic at all, but instead reflects visual-visual interactions jumpstarted at the very first stage of visual processing in the brain.