  Theoretical studies of cosmic ray particle acceleration in the first-order
Fermi process at relativistic shocks are reviewed. At the beginning we discuss
the acceleration processes acting at mildly relativistic shock waves. An
essential role of oblique field configurations and field perturbations in
forming the particle energy spectrum and changing the acceleration time scale
is discussed. Then, we report on attempts to consider particle acceleration at
ultra-relativistic shocks, often yielding an asymptotic spectral index sigma =
2.2 at large shock Lorentz factors. We explain why this result is limited to
the cases of highly turbulent conditions near shocks. We conclude that our
present knowledge of the acceleration processes acting at relativistic shocks
is insufficient to allow for realistic modelling of the real shocks. The
present review is a modified, extended and updated version of Ostrowski (1999).
