  We review recent progress on collisionless relativistic shocks. Kinetic
instability theory is briefed including its predictions and limitations. The
main focus is on numerical experiments in (i) pair and (ii) electron-nucleon
plasmas. The main results are: (i) confirmation of shock evolution in
non-magnetised relativistic plasma in 3D due to either the lepton-Weibel
instability or the ion-Weibel instability; (ii) sensitive dependence on
upstream magnetisation ; (iii) the sensitive dependence of particle dynamics on
the upstream magnetic inclination angle $\thetabn$, where particles of
$\thetabn>34^\circ$ cannot escape upstream, leading to the distinction between
`sub-luminal' and `super-luminal' shocks; (iv) particles in ultra-relativistic
shocks can hardly overturn the shock and escape to upstream; they may oscillate
around the shock ramp for a long time, so to speak `surfing it' and thereby
becoming accelerated by a kind of SDA; (v) these particles form a power law
tail on the downstream distribution; their limitations are pointed out; (vi)
recently developed methods permit the calculation of the radiation spectra
emitted by the downstream high-energy particles; (vii) the Weibel-generated
downstream magnetic fields form large amplitude vortices which could be
advected by the downstream flow to large distances from the shock and possibly
contribute to an extended strong field region; (viii) if cosmic rays are
included, Bell-like modes can generate upstream magnetic turbulence at short
and, by diffusive re-coupling, also long wavelengths in nearly parallel
magnetic field shocks; (ix) advection of such large-amplitude waves should
cause periodic reformation of the quasi-parallel shock and eject large
amplitude magnetic field vortices downstream where they contribute to
turbulence and to maintaining an extended region of large magnetic fields.
