  Giant radio halos in galaxy clusters probe mechanisms of particle
acceleration connected with cluster merger events. Shocks and turbulence are
driven in the inter-galactic-medium (IGM) during clusters mergers and may have
a deep impact on the non-thermal properties of galaxy clusters. Models of
turbulent (re)acceleration of relativistic particles allow good correspondence
with present observations, from radio halos to gamma-ray upper limits, although
several aspects of this complex scenario remain still poorly understood. After
providing basic motivations for turbulent acceleration in galaxy clusters, we
discuss relevant aspects of the physics of particle acceleration by MHD
turbulence and the expected broad--band non-thermal emission from galaxy
clusters. We discuss (in brief) the most important results of turbulent
(re)acceleration models, the open problems, and the possibilities to test
models with future observations. In this respect, further constraints on the
origin of giant nearby radio halos can also be obtained by combining their
(spectral and morphological) properties with the constraints from gamma-ray
observations of their parent clusters.
