Non-thermal phenomena in galaxies clusters

The discovery of diffuse synchrotron radio emission and, more recently, of the hard X-ray (HXR) tails have triggered a growing interest about non-thermal phenomena in galaxy clusters. After a brief review of the most important evidences for non-thermal emission, I will focus on the origin of the emitting particles and of the hadronic component. In particular I will describe the particle-injection and -acceleration mechanisms at work in the intra-cluster medium (ICM) and, at the same time, discuss the possibility to test current modellings of these phenomena with future radio, HXR, and gamma rays observatories.