  We review the basic features of particle acceleration theory around
collisionless shocks in supernova remnants (SNRs). We show how non linear
effects induced by the back reaction of accelerated particles onto the shock
dynamics are of paramount importance to support the hipotesys that SNRs are the
factories of Galactic cosmic rays. Recent developments in the modeling of the
mechanism of diffusive shock acceleration are discussed, with emphasis on the
role of magnetic field amplification and the presence of neutrals in the
circumstellar environment. Special attention will be devoted to observational
consequences of non linear effects on the multi-wavelength spectrum of SNRs,
with emphasis on X-ray and gamma-ray emission. Finally we also discuss how
Balmer lines, detected from several young SNRs, can be used to estimate the
shock dynamical properties and the efficiency of CR acceleration.
