[en] Briefly reviewed are the main processes of fast particle interaction with the shock front, namely the relative role of the Fermi acceleration the acceleration by the regular electric field of the shock wave, and also the reflection of particles from the shock front. The equations and the boundary conditions for the phase density of particles in the shock front are derived. These equations provide for a strict formulation of the problems of particle transfer and acceleration in the turbulent medium in the presence of sharp shock fronts, as well as of rarefaction waves and other large-scale disturbances. The solutions of this problem for a few simplest onedimensional cases are presented. The problem of the formation of the accelerated particle spectra in the interplanetary space and in the supernovae remnants, including the formation of the power-like spectra with weak dependence on the detailed mechanism of acceleration, is discussed. Some possible manifestations of the acceleration mechanism considered in galactic and extra-galactic radio-sources are pointed out