  A comprehensive review is given of the various processes proposed for
accelerating particles by shocks to high energies. These energies are limited
by several bounds: the non-relativistic nature of the heliospheric
collisionless shocks to which this review restricts, the finite size of these
shocks, the finite width of the downstream region, and to the nature of
turbulence. In general, collisionless shocks in the heliosphere cannot
accelerate particles to very high energies. As a fundamental problem of the
acceleration mechanism the injection of see particles is identified. Some
mecchanisms for production of seed particles are invoked. Acceleration of
electrons begins to uncover its nature. The following problems are covered in
this chapter: 1. Introduction -- first and second order Fermi acceleration, 2.
Accelerating ions when they are already fast, diffusive acceleration,
convection diffusion equation, Lee's self-consistent quasilinear shock
acceleration model, 3. Observations, 4. The injection problem, ion surfing,
test particle simulations, self-consistent shock acceleration simulations,
downstream leakage, trapped particle acceleration, 5. Accelerating electrons,
Sonnerup-Wu mechanism, Hoshino's electron shock surfing on quasi-perpendicular
shocks, quasiparallel shock surfing.
