  Relativistic astrophysical collisionless shocks represent outstanding
dissipation agents of the huge power of relativistic outflows produced by
accreting black holes, core collapsed supernovae and other objects into
multi-messenger radiation (cosmic rays, neutrinos, electromagnetic radiation).
This article provides a theoretical discussion of the fundamental physical
ingredients of these extreme phenomena. In the context of weakly magnetized
shocks, in particular, it is shown how the filamentation type instabilities,
which develop in the precursor of pair dominated or electron-ion shocks,
provide the seeds for the scattering of high energy particles as well as the
agent which preheats and slows down the incoming precursor plasma. This
analytical discussion is completed with a mesoscopic, non-linear model of
particle acceleration in relativistic shocks based on Monte Carlo techniques.
This Monte Carlo model uses a semi-phenomenological description of particle
scattering which allows it to calculate the back-reaction of accelerated
particles on the shock structure on length and momentum scales which are
currently beyond the range of microscopic particle-in-cell (PIC) simulations.
