  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. We discuss here 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. 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. 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.
