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 \approx 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 ) .

Key words : cosmic rays – relativistic shock waves – gamma ray bursts

PACS numbers : 95.30.Qd , 95.85.Pw , 98.70.Rz , 98.70.Sa