The existence and extent of non-thermal phenomena in galaxy clusters is now well established. A key question in our understanding of these phenomena is the origin of the relativistic electrons which may be constrained by the modelling of the fine radio properties of radio halos and of their statistics. In this paper we argue that present data favour a scenario in which the emitting electrons in the intracluster medium (ICM) are reaccelerated in situ on their way out. An overview of turbulent-particle acceleration models is given focussing on recent time-dependent calculations which include a full coupling between particles and MHD waves.