  Clusters of galaxies are storage rooms of cosmic rays. They confine the
hadronic component of cosmic rays over cosmological time scales due to
diffusion, and the electron component due to energy losses. Hadronic cosmic
rays can be accelerated during the process of structure formation, because of
the supersonic motion of gas in the potential wells created by dark matter. At
the shock waves that result from this motion, charged particles can be
energized through the first order Fermi process. After discussing the most
important evidences for non-thermal phenomena in large scale structures, we
describe in some detail the main issues related to the acceleration of
particles at these shock waves, emphasizing the possible role of the dynamical
backreaction of the accelerated particles on the plasmas involved.
