  We review the physics of relativistic shocks, which are often invoked as the
sources of non-thermal particles in pulsar wind nebulae (PWNe), gamma-ray
bursts (GRBs), and active galactic nuclei (AGN) jets, and as possible sources
of ultra-high energy cosmic-rays. We focus on particle acceleration and
magnetic field generation, and describe the recent progress in the field driven
by theory advances and by the rapid development of particle-in-cell (PIC)
simulations. In weakly magnetized or quasi parallel-shocks (where the magnetic
field is nearly aligned with the flow), particle acceleration is efficient. The
accelerated particles stream ahead of the shock, where they generate strong
magnetic waves which in turn scatter the particles back and forth across the
shock, mediating their acceleration. In contrast, in strongly magnetized
quasi-perpendicular shocks, the efficiencies of both particle acceleration and
magnetic field generation are suppressed. Particle acceleration, when
efficient, modifies the turbulence around the shock on a long time scale, and
the accelerated particles have a characteristic energy spectral index of ~ 2.2
in the ultra-relativistic limit. We discuss how this novel understanding of
particle acceleration and magnetic field generation in relativistic shocks can
be applied to high-energy astrophysical phenomena, with an emphasis on PWNe and
GRB afterglows.
