The thermal component of the Inter-Galactic-Medium (IGM) in galaxy clusters is mixed with non-thermal components such as magnetic fields and relativistic particles. These components may play a key role by controlling transport processes in the IGM and are sources of additional pressure, thus they have the potential to affect our simplified view of the physics of the IGM. After a brief review of the most relevant observational facts that already put constraints on the properties and origin of non-thermal components, I will focus on theoretical aspects and report on models of particle acceleration and non thermal emission in galaxy clusters. In particular I will discuss a general modeling in which relativistic particles (protons and secondary electrons due to proton-proton collisions) interact with MHD turbulence generated in the cluster volume during cluster-cluster mergers. In this scenario (known as re-acceleration scenario) diffuse cluster-scale radio emission (Radio Halos) and hard X-ray emission are produced in massive clusters during merging events, while gamma ray emission, at some level, is expected to be common in clusters. In next years LOFAR and GLAST will provide crucial information on the non-thermal components in galaxy clusters and I will discuss model expectations that will be tested by these instruments. Il seminario si terra' nella sala adiacente alla direzione