For more than a decade already and because of their technological potential for incorporation in spintronic devices, diluted magnetic semiconductors (dmS’s) have attracted a considerable attention from both experimentalists and theoreticians. a very competitive race started with the discovery that a very small amount of mn (which introduces a 3d5 configuration + itinerant hole) in thin films of the iii-V semiconductor Gaas could lead to a relatively high curie temperature ferromagnet. (Ga,mn)as rapidly became the most studied prototype, which still exhibits (for a given mn density and well annealed samples) the highest critical temperature among iii-V dmS compounds (190 K). However, even today, from the physical understanding and theoretical point of view, one often finds contradicting theories and results in the literature. Full text