  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.
