  Relativistic sources, e.g. gamma-ray bursts, pulsar wind nebulae and powerful
active galactic nuclei produce relativistic outflows that lead to the formation
of collisionless shock waves, where particle acceleration is thought to take
place. Our understanding of relativistic shock acceleration has improved in the
past decade, thanks to the combination of analytical studies and high level
numerical simulations. In ultra-relativistic shocks, particle acceleration is
made difficult by the generically transverse magnetic field and large advection
speed of the shocked plasma. Fast growing microturbulence is thus needed to
make the Fermi process operative. It is thought, and numerical simulations
support that view, that the penetration of supra-thermal particles in the shock
precursor generates a magnetic turbulence which in turn produces the scattering
process needed for particle acceleration through the Fermi mechanism. Through
the comparison of the growth timescale of the microinstabilities in the shock
precursor and the precursor crossing timescale, it is possible to delimit in
terms of magnetization and shock Lorentz factor the region in which
micro-turbulence may be excited, hence whether and how Fermi acceleration is
triggered. These findings are summarized here and astrophysical consequences
are drawn.
