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.

• PASQUALE BLASI(INAF/Osservatorio Astrofisico di Arcetri)