When you look into a mirror and move your eyes left to right, you will see that you cannot observe your own eye movements. This demonstrates the phenomenon of saccadic suppression: during saccadic eye movements, visual sensitivity is much reduced. Given that humans make more than 100,000 eye movements each day, it is clear why suppression is needed: without it, the motion on the retina would prevent us from seeing anything at all. Psychophysical data show that suppression is stimulus selective: it is strongest for the kind of stimuli that preferentially activate magnocellular thalamic neurons. This has led to the hypothesis that saccadic suppression selectively targets the magnocellular stream. We used fMRI to find brain areas with a stimulus-selective suppression of the BOLD signal that matches the psychophysical data. We found such a neural correlate of saccadic suppression in the dorsal stream (hMT+, V7) and in ventral area V4. These areas receive magnocellular input; hence our findings are consistent with the magnocellular hypothesis. The range of effects in our data and in single cell data, however, argues against a single thalamic mechanism that suppresses all cortical input. Instead, we speculate that saccadic suppression relies on multiple mechanisms operating in different cortical areas.