The diffusive shock acceleration mechanism is invoked to explain on-thermalcosmic rays in Supernova Remnants, Active Galactic Nuclei Jets and Gamma-ray Bursts. Especially, the importance of achieving the highest observed cosmic ray energies by such a mechanism in a given astrophysical environment is a recurring theme. In this talk, Monte Carlo simulation studies of cosmic ray acceleration in relativistic subluminal and superluminal shocks will be presented, with an emphasis on the acquired diffuse cosmic ray signal at the highest energies observed, and the role of the efficiency of various classes of relativistic shocks will be discussed.
