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 ray observatories.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html