Avoiding predators is an essential behavior in which animals must quickly transform sensory cues into evasive actions. Sensory reflexes are particularly fast in flying insects such as flies, but the means by which they evade aerial predators is not known. Using high-speed videography and automated tracking of flies in combination with aerodynamic measurements on flapping robots, we show that flying flies react to looming stimuli with directed banked turns. The maneuver consists of a rapid body rotation followed immediately by an active counter-rotation and is enacted by remarkably subtle changes in wing motion. These evasive maneuvers of flies are substantially faster than steering maneuvers measured previously and indicate the existence of sensory-motor circuitry that can reorient the fly's flight path within a few wingbeats.