Cosmic-ray acceleration, although physically important in many astrophysical contexts, is difficult to incorporate into numerical models,. because it involves microphysics that is generally far from thermodynamic equilibrium, and also because the length and time scales for that physics typically range over many orders of magnitude, reflecting the huge range of particle rigidities that must be represented. The most common accelerator models are stochastic in nature and involve nonequilibrium plasma properties that are also often poorly understood. Still, nature clearly finds a way to produce simple, robust and almost scale-free energy distributions for the cosmic-rays. Their importance has inspired a number of approaches to examining the production and transport of cosmic-ray particles in numerical simulations. I offer here a brief comparison of some of the methods that have been introduced.

Rarefied cosmic plasmas generally do not achieve thermodynamic equilibria, and a natural consequence of this is the presence of a significant population of charged particles with energies well above those of the bulk population. These are exemplified by the galactic cosmic rays, but the importance of these high energy populations extends well beyond that context. I review here some of the basic issues associated with the propagation and acceleration of cosmic rays, especially in the context of collisionless plasma shocks.