A trapeze is a short horizontal bar suspended from two parallel ropes. Flying trapeze is an act involving two trapezes: the catcher's bar and the fly bar. The catcher's bar is at one end of the rig. The fly bar is more central. At the opposite end from the catcher's bar is a pedestal.

The flyer jumps from a pedestal, holding on to the fly bar. After the appropriate number of swings, the flyer often releases the fly bar and is caught by another performer, the "catcher," who hangs by his knees on another trapeze, the “catcher’s bar," or sometimes on a cradle, which can be either stationary or also swinging. After a swing, the catcher returns the flyer to the fly bar. The act is done high above the ground requires excellent timing in order to achieve the catch.

The flying trapeze was invented in the late 19th Century in France by Jules Léotard, who is also said to have invented the full length skin-tight costume that now bears his name.