Insects have evolved sophisticated reflexes to right themselves in mid-air. Their recovery mechanisms involve complex interactions among the physical senses, muscles, body, and wings, and they must obey the laws of flight. We sought to understand the key mechanisms involved in dragonfly righting reflexes and to develop physics-based models for understanding the control strategies of flight maneuvers. Using kinematic analyses, physical modeling, and three-dimensional flight simulations, we found that a dragonfly uses left-right wing pitch asymmetry to roll its body 180 degrees to recover from falling upside down in ~200 milliseconds. Experiments of dragonflies with blocked vision further revealed that this rolling maneuver is initiated by their ocelli and compound eyes. These results suggest a pathway from the dragonfly's visual system to the muscles regulating wing pitch that underly the recovery. The methods developed here offer quantitative tools for inferring insects' internal actions from their acrobatics, and are applicable to a broad class of natural and robotic flying systems.