  A plasma velocity shear layer and/or a tangential flow discontinuity provide
conditions allowing for energetic particle acceleration. We review such
acceleration processes acting both in non-relativistic and in relativistic
flows. In heliospheric conditions shear layers can provide particles with
energies compatible with the observed values (from several keV up to MeV),
while in relativistic extragalactic jets proton energies even in excess of
10^{19} eV can be obtained. Application of the discussed theory to particular
astrophysical objects is severely limited by inadequate knowledge of local
physical conditions.
