Moving highly-charged ions carry strong electromagnetic fields that act as a
field of photons. In collisions at large impact parameters, hadronic
interactions are not possible, and the ions interact through photon-ion and
photon-photon collisions known as {\it ultra-peripheral collisions} (UPC).
Hadron colliders like the Relativistic Heavy Ion Collider (RHIC), the Tevatron
and the Large Hadron Collider (LHC) produce photonuclear and two-photon
interactions at luminosities and energies beyond that accessible elsewhere; the
LHC will reach a γp energy ten times that of the Hadron-Electron Ring
Accelerator (HERA). Reactions as diverse as the production of anti-hydrogen,
photoproduction of the ρ0, transmutation of lead into bismuth and
excitation of collective nuclear resonances have already been studied. At the
LHC, UPCs can study many types of `new physics.'Comment: 47 pages, to appear in Annual Review of Nuclear and Particle Scienc