The observed properties of high energy particles in different astrophysical environments are briefly summarized. It appears that cosmic rays are freely produced with high (up to 10 per cent) efficiency by supersonic flows. At relativistic energies, the integral distribution function of the accelerated particles (i.e., the number of particles with energy in excess of some value E) generally has a power law form with slope lying in the range ∼1.2 to 1.8. Various particle acceleration schemes are examined. Fermi acceleration at strong shock fronts seems a particularly promising process. A simple test particle analysis suggests that this mechanism can fulfill the necessary energetic and spectral requirements of galactic cosmic rays. More detailed studies of shock acceleration including the mediating influence of the accelerated particles and the generation of scattering Alfven modes together with models of the gas subshock give inconclusive results. Future progress depends upon combining the results of in sit...