There is now firm evidence that the ICM consists of a mixture of hot plasma, magnetic fields and relativistic particles. The most important pieces of evidence for non-thermal phenomena in galaxy clusters come from the diffuse Mpc-scale synchrotron radio emission (radio halos), observed in a growing number of massive clusters (Feretti 2003), and from hard X-ray (HXR) excess emission (detected in a few cases), which can be explained in terms of IC scattering of relativistic electrons off the cosmic microwave background photons (Fusco-Femiano et al. 2003). There is now growing evidence that giant radio halos may be naturally accounted for by synchrotron emission from relativistic electrons reaccelerated by some kind of turbulence generated in the cluster volume during merger events (Brunetti 2003). With the aim of investigating the connection between thermal and non-thermal properties of the ICM, we have developed a statistical magneto-turbulent model which describes the evolution of the thermal and non-thermal emission from clusters. We calculate the energy and spectrum of the magne-!tosonic waves generated during cluster mergers, the acceleration and evolution of relativistic electrons and thus the resulting synchrotron and inverse Compton spectra. Here we give a brief description of the main results, while a more detailed discussion will be presented in a forthcoming paper (Cassano & Brunetti, in preparation). Einstein-De Sitter cosmology, $H_0=50$ km s$^{-1}$ Mpc$^{-1}$, $q_0=0.5$, is assumed.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html