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Giant radio halos in galaxy clusters probe mechanisms of particleacceleration connected with cluster merger events. Shocks and turbulence aredriven in the inter-galactic-medium (IGM) during clusters mergers and may havea deep impact on the non-thermal properties of galaxy clusters. Models ofturbulent (re)acceleration of relativistic particles allow good correspondencewith present observations, from radio halos to gamma-ray upper limits, althoughseveral aspects of this complex scenario remain still poorly understood. Afterproviding basic motivations for turbulent acceleration in galaxy clusters, wediscuss relevant aspects of the physics of particle acceleration by MHDturbulence and the expected broad--band non-thermal emission from galaxyclusters. We discuss (in brief) the most important results of turbulent(re)acceleration models, the open problems, and the possibilities to testmodels with future observations. In this respect, further constraints on theorigin of giant nearby radio halos can also be obtained by combining their(spectral and morphological) properties with the constraints from gamma-rayobservations of their parent clusters.

Giant radio halos in galaxy clusters as probes of particle acceleration in turbulent regions