Psychophysical studies have shown that subjects are often unaware of visual stimuli presented around the time of an eye movement. This saccadic suppression is thought to be a mechanism for maintaining perceptual stability. The brain might accomplish saccadic suppression by reducing the gain of visual responses to specific stimuli or by simply suppressing firing uniformly for all stimuli. Moreover, the suppression might be identical across the visual field or concentrated at specific points. To evaluate these possibilities, we recorded from individual neurons in cortical area V4 of nonhuman primates trained to execute saccadic eye movements. We found that both modes of suppression were evident in the visual responses of these neurons and that the two modes showed different spatial and temporal profiles: while gain changes started earlier and were more widely distributed across visual space, nonspecific suppression was found more often in the peripheral visual field, after the completion of the saccade. Peripheral suppression was also associated with increased noise correlations and stronger local field potential oscillations in the α frequency band. This pattern of results suggests that saccadic suppression shares some of the circuitry responsible for allocating voluntary attention. We explore our surroundings by looking at things, but each eye movement that we make causes an abrupt shift of the visual input. Why doesn't the world look like a film recorded on a shaky camera? The answer in part is a brain mechanism called saccadic suppression, which reduces the responses of visual neurons around the time of each eye movement. Here we reveal several new properties of the underlying mechanisms. First, the suppression operates differently in the central and peripheral visual fields. Second, it appears to be controlled by oscillations in the local field potentials at frequencies traditionally associated with attention. These results suggest that saccadic suppression shares the brain circuits responsible for actively ignoring irrelevant stimuli.