We present a fluid dynamics video showing simulations of flexible bodies flapping and falling in an inviscid fluid. Vortex sheets are shed from the trailing edges of the bodies according to the Kutta condition. For interacting flags, a sampling of synchronous and asynchronous states are shown. For falling flexible sheets, the basic behavior is a repeated series of accelerations to a critical speed at which the sheet buckles, and rapidly decelerates, shedding large vortices. Examples of persistent circling, quasi-periodic flapping, and more complex patterns are shown.