Due to coherence, there are strong electromagnetic fields of short duration in very peripheral collisions. They give rise to photon-photon and photon-nucleus collisions with high flux up to an invariant mass region hitherto unexplored experimentally. After a general survey photon-photon luminosities in relativistic heavy ion collisions are discussed. Special care is taken to include the effects of strong interactions and nuclear size. Then photon-photon physics at various invariant mass scales is discussed. Invariant masses of up to about 100 GeV can be reached at LHC, and in addition the potential for new physics is available. Photonuclear reactions and other important background effects, especially diffractive processes are also discussed. Lepton-pair production, especially electron-positron pair production is copious. Due to the strong fields there will be new phenomena, especially multiple e+e- pair production.
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