INSECTS cannot fly, according to the conventional laws of aerodynamics: during flapping flight, their wings produce more lift than during steady motion at the same velocities and angles of attack1-5. Measured instantaneous lift forces also show qualitative and quantitative disagreement with the forces predicted by conventional aerodynamic theories6-9. The importance of high-life aerodynamic mechanisms is now widely recognized but, except for the specialized fling mechanism used by some insect species1,10-13, the source of extra lift remains unknown. We have now visualized the airflow around the wings of the hawkmoth Manduca sexta and a 'hovering' large mechanical model-the flapper. An intense leading-edge vortex was found on the down-stroke, of sufficient strength to explain the high-lift forces. The vortex is created by dynamic stall, and not by the rotational lift mechanisms that have been postulated for insect flight14-16. The vortex spirals out towards the wingtip with a spanwise velocity comparable to the flapping velocity. The three-dimensional flow is similar to the conical leading-edge vortex found on delta wings, with the spanwise flow stabilizing the vortex.