  Carrier-induced ferromagnetism has been observed in several (III,Mn)V
semiconductors. We review the theoretical picture of these ferromagnetic
semiconductors that emerges from a model with kinetic-exchange coupling between
localized Mn spins and valence-band carriers. We discuss the applicability of
this model, the validity of a mean-field approximation for its interaction term
widely used in the literature, and validity limits for the simpler RKKY model
in which only Mn spins appear explicitly. Our conclusions are based in part on
our analysis of the dependence of the system's elementary spin excitations on
carrier density and exchange-coupling strength. The analogy between this system
and spin-model ferrimagnets is explored. Finally, we list several extensions of
this model that can be important in realistic modeling of specific materials.
