  We present some recent developments in the theory of particle acceleration at
shock fronts in the presence of dynamical reaction of the accelerated particles
and self-generation of magnetic field due to streaming instability. The spectra
of accelerated particles, the velocity, magnetic field and temperature profiles
can be calculated in this approach anywhere in the precursor and in the
downstream region. The implications for the origin of cosmic rays and for the
phenomenology of supernova remnants will be discussed.

Astrophysics