Particle acceleration and relativistic shocks

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.