Saccadic eye movements play a central role in primate vision. Yet, relatively little is known about their effects on the neural processing of visual inputs. Here we examine this question in primary visual cortex (V1) using receptive-field-based models, combined with an experimental design that leaves the retinal stimulus unaffected by saccades. This approach allows us to analyse V1 stimulus processing during saccades with unprecedented detail, revealing robust perisaccadic modulation. In particular, saccades produce biphasic firing rate changes that are composed of divisive gain suppression followed by an additive rate increase. Microsaccades produce similar, though smaller, modulations. We furthermore demonstrate that this modulation is likely inherited from the LGN, and is driven largely by extra-retinal signals. These results establish a foundation for integrating saccades into existing models of visual cortical stimulus processing, and highlight the importance of studying visual neuron function in the context of eye movements.