Moffatt has argued [J. Fluid. Mech.218, 509 (1990)] that it should be possible to control the motion of a metallic sphere immersed in a nonconducting fluid using the electromagnetic force and couple generated by means of a traveling and/or rotating magnetic field applied externally. Such a system has been realized experimentally: one or more aluminum spheres are placed in a vessel containing fluid (air, water, or silicone oil), the whole being placed in an inductor which provides an upward‐traveling magnetic field. The spheres move in response to the induced electromagnetic forces, the motion being influenced by gravity, viscous drag, vessel boundary reaction, and collisions. A range of possible behaviors, stable, unstable, and chaotic, are identified and discussed. The term ‘‘electromagnetic billiards’’ seems appropriate to describe this phenomenon.