  Particle acceleration in collisionless shocks is believed to be responsible
for the production of cosmic-rays over a wide range of energies, from few GeV
to >10^{20}eV, as well as for the non-thermal emission of radiation from a wide
variety of high energy astrophysical sources. A theory of collisionless shocks
based on first principles does not, however, exist. Observations of gamma-ray
burst (GRB) "afterglows" provide a unique opportunity for diagnosing the
physics of relativistic collisionless shocks. Most GRBs are believed to be
associated with explosions of massive stars. Their "afterglows," delayed low
energy emission following the prompt burst of gamma-rays, are well accounted
for by a model in which afterglow radiation is due to synchrotron emission of
electrons accelerated in relativistic collisionless shock waves driven by the
explosion into the surrounding plasma. Within the framework of this model, some
striking characteristics of collisionless relativistic shocks are implied.
These include the generation of downstream magnetic fields with energy density
exceeding that of the upstream field by ~8 orders of magnitude, the survival of
this strong field at distances ~10^{10} skin-depths downstream of the shock,
and the acceleration of particles to a power-law energy spectrum, d\log n/d\log
E ~ -2, possibly extending to 10^{20}eV. I review in this talk the
phenomenological considerations, based on which these characteristics are
inferred, and the challenges posed to our current models of particle
acceleration and magnetic field generation in collisionless shocks. Some recent
theoretical results derived based on the assumption of a self-similar shock
structure are briefly discussed.
