Recent materials research has advanced the maximum ferromagnetic transition temperature in semiconductors containing magnetic elements toward room temperature. Reaching this goal would make information technology applications of these materials likely. In this article we briefly review the status of work over the past five years which has attempted to achieve a theoretical understanding of these complex magnetic systems. The basic microscopic origins of ferromagnetism in the (III,Mn)V compounds that have the highest transition temperatures appear to be well understood, and efficient computation methods have been developed which are able to model their magnetic, transport, and optical properties. However many questions remain.It is hoped that the emerging field of semiconductor spintronics, which studies the controlled flow of charge and spin in a semiconductor, will lead to the development of new non-volatile, high-density, and high-speed information technologies. An important milestone in this field was the discovery five years ago of ferromagnetism in Mn-doped, p-type GaAs observed at temperatures in excess of 100 Kelvin [1]. Ferromagnetism at room temperature with full participation of itinerant carriers would be a major breakthrough in semiconductor spintronics. With this aim, intensive material research is currently in progress on transition metal doped III-V semiconductors. In this brief review we present a snap shot of the theoretical part of this endeavor, which has progressed hand in hand with experimental developments.A qualitative picture of the electronic structure of III-V diluted magnetic semiconductors (DMSs) was proposed by Dietl and coworkers [2,3]. Their model is based on the internal reference rule [6] which states that energy levels derived from the d-shell of the magnetic ion are constant across semiconductor compound families with properly aligned bands. The application of this rule to III-V materials is illustrated in Fig 1 for ionized magnetic impurities substituted on cation sites [2][3][4][5]. The position of the A 2 level for Mn in GaAs, deep in the valence band, suggests that Mn in GaAs is 2+, that its d-shell is occupied by five electrons, and that incorporation of Mn in this and many other (III,Mn)V compounds will result a large density of valence band holes that can mediate ferromagnetic coupling between the S = 5/2 Mn local moments. For low carrier densities, these valence band holes will be bound to the Mn ion, leading to shallow acceptor levels. This model of carrier-induced ferromagnetism is now fairly well established for (Ga,Mn)As as a result of electron paramagnetic resonance experiments [7], xray magnetic circular dichroism measurements [8,9], and magneto-transport data [10-13].The acceptor impurity levels of Fe and Co [2,3,6,4] are unlikely to lead to high valence band hole concentrations in arsenides or antimonides, as shown in Fig. 1. The possible coexistence of acceptor and neutral magnetic impurities suggests that a ferromagnetic double-exchange mechanism can dominate ...