  The first electromagnetic signal observed in different types of cosmic
explosions is released upon emergence of a shock created in the explosion from
the opaque envelope enshrouding the central source. Notable examples are the
early emission from various types of supernovae and low luminosity GRBs, the
prompt photospheric emission in long GRBs, and the gamma-ray emission that
accompanied the gravitational wave signal in neutron star mergers. In all of
these examples, the shock driven by the explosion is mediated by the radiation
trapped inside it, and its velocity and structure, that depend on environmental
conditions, dictate the characteristics of the observed electromagnetic
emission at early times, and potentially also their neutrino emission. Much
efforts have been devoted in recent years to develop a detailed theory of
radiation mediated shocks in an attempt to predict the properties of the early
emission in the aforementioned systems. These efforts are timely in view of the
anticipated detection rate of shock breakout candidates by upcoming transient
factories, and the potential detection of a gamma-ray flash from shock breakout
in neutron star mergers like GW170817. This review aims at providing a
comprehensive overview of the theory and applications of radiation mediated
shocks, starting from basic principles. The classification of shock solutions,
which are governed by the conditions prevailing in each class of objects, and
the methods used to solve the shock equations in different regimes will be
described, with particular emphasis on the observational diagnostics. The
applications to supernovae, low-luminosity GRBs, long GRBs, neutron star
mergers, and neutrino emission will be highlighted.
