  In central collisions at relativistic heavy ion colliders like the
Relativistic Heavy Ion Collider RHIC/Brookhaven and the Large Hadron Collider
LHC (in its heavy ion mode) at CERN/Geneva, one aims at detecting a new form of
hadronic matter - the Quark Gluon Plasma. It is the purpose of this review to
discuss a complementary aspect of these collisions, the very peripheral ones.
Due to coherence, there are strong electromagnetic fields of short duration in
such 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 gamma-gamma-invariant mass scales is discussed. The region
of several GeV, relevant for RHIC is dominated by QCD phenomena (meson and
vector meson pair production). Invariant masses of up to about 100 GeV can be
reached at LHC, and the potential for new physics is discussed. Photonuclear
reactions and other important background effects, especially diffractive
processes are also discussed. A special chapter is devoted to lepton-pair
production, especially electron-positron pair production; due to the strong
fields new phenomena, especially multiple e+-e- pair production, will occur
there.
