Most animals have compound eyes, with tens to thousands of lenses attached rigidly to the exoskeleton. A natural assumption is that all of these species must resort to moving either their head or their body to actively change their visual input. However, classic anatomy has revealed that flies have muscles poised to move their retinas under the stable lenses of each compound eye1–3. Here we show that Drosophila use their retinal muscles to smoothly track visual motion, which helps to stabilize the retinal image, and also to perform small saccades when viewing a stationary scene. We show that when the retina moves, visual receptive fields shift accordingly, and that even the smallest retinal saccades activate visual neurons. Using a head-fixed behavioural paradigm, we find that Drosophila perform binocular, vergence movements of their retinas—which could enhance depth perception—when crossing gaps, and impairing the physiology of retinal motor neurons alters gap-crossing trajectories during free behaviour. That flies evolved an ability to actuate their retinas suggests that moving the eye independently of the head is broadly paramount for animals. The similarities of smooth and saccadic movements of the Drosophila retina and the vertebrate eye highlight a notable example of convergent evolution. Drosophila are shown to have retinal muscles that allow them to smoothly track visual motion and also to make rapid eye movements, and the associated functions and mechanisms involved are discussed.