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.
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