  Observations of both gamma-ray burst sources and certain classes of active
galaxy indicate the presence of relativistic shock waves and require the
production of high energy particles to explain their emission. In this paper we
review the basic theory of shock waves in relativistic hydrodynamics and
magneto-hydrodynamics, emphasising the astrophysically interesting cases. This
is followed by an overview of the theory of particle acceleration at such
shocks. We summarise the applications to the astrophysics of relativistic jets
and fireball models of gamma-ray-bursts.
