Humans use saccadic eye movements to make frequent gaze changes, yet the associated full-field image motion is not perceived. The theory of saccadic suppression has been proposed to account for this phenomenon, but it is not clear whether suppression originates from a retinal signal at saccade onset or from the brain before saccade onset. Perceptually, visual sensitivity is reduced before saccades and enhanced afterward. Over the same time period, the perception of time is compressed and even inverted. We explore the origins and neural basis of these effects by recording from neurons in the dorsal medial superior temporal area (MSTd) of alert macaque monkeys. Neuronal responses to flashed presentations of a textured pattern presented at random times relative to saccades exhibit a stereotypical pattern of modulation. Response amplitudes are strongly suppressed for flashes presented up to 90 ms before saccades. Immediately after the suppression, there is a period of 200-450 ms in which flashes generate enhanced response amplitudes. Our results show that (1) MSTd is not directly suppressed, rather suppression is inherited from earlier visual areas; (2) early suppression of the visual system must be of extra-retinal origin; (3) postsaccadic enhancement of neural activity occurs in MSTd; and (4) the enhanced responses have reduced latencies. As a whole, these observations reveal response properties that could account for perceptual observations relating to presaccadic suppression, postsaccadic enhancement and time compression.