  Direct photons have been proposed as a promising signature for the
quark-gluon plasma (QGP) formation in relativistic heavy-ion collisions.
Recently WA98 presented the first data on direct photons in Pb+Pb-collisions at
SPS. At the same time RHIC started with its experimental program. The discovery
of the QGP in these experiments relies on a comparison of data with theoretical
predictions for QGP signals. In the case of direct photons new results for the
production rates of thermal photons from the QGP and a hot hadron gas as well
as for prompt photons from initial hard parton scatterings have been proposed
recently. Based on these rates a variety of different hydrodynamic models,
describing the space-time evolution of the fireball, have been adopted for
calculating the direct photon spectra. The results have been compared to the
WA98 data and predictions for RHIC and LHC have been made. So far the
conclusions of the various models are controversial.
  The aim of the present review is to provide a comprehensive and up-to-date
survey and status report on the experimental and theoretical aspects of direct
photons in relativistic heavy-ion collisions.
