Ultra-peripheral collisions of relativistic heavy ions involve long-ranged
electromagnetic interactions at impact parameters too large for hadronic
interactions to occur. The nuclear charges are large; with the coherent
enhancement, the cross sections are also large. Many types of photonuclear and
purely electromagnetic interactions are possible. We present here an
introduction to ultra-peripheral collisions, and present four of the most
compelling physics topics. This note developed from a discussion at a workshop
on ``Electromagnetic Probes of Fundamental Physics,'' in Erice, Italy, Oct.