  It is well accepted today that diffusive acceleration in shocks results to
the cosmic ray spectrum formation. This is in principle true for
non-relativistic shocks, since there is a detailed theory covering a large
range of their properties and the resulting power-law spectrum, which is
nevertheless not as efficient to reach the very high energies observed in the
cosmic ray spectrum. On the other hand, the cosmic ray maximum energy and the
resulting spectra from relativistic shocks, are still under investigation and
debate concerning their contribution to the features of the cosmic ray spectrum
and the measured, or implied, cosmic ray radiation from candidate astrophysical
sources. Here, we discuss the efficiency of the first order Fermi (diffusive)
acceleration mechanism up to relativistic shock speeds, presenting Monte Carlo
simulations.
