  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.
