The present chapter discusses the properties of III–V diluted magnetic semiconductors (DMS) and their theoretical understanding. By DMS, we mean semiconducting compounds doped with magnetic ions and showing ferromagnetic order below a Curie temperature T C . Due to the semiconducting properties of DMS, the carrier concentration can be changed significantly by doping, and even in situ by the application of a gate voltage, or by optical excitations. Since the carriers couple strongly to the magnetic moments, this leads to unique properties, and makes DMS promising for spintronics. In particular, magnetotransport and spin transfer in DMS-based devices are discussed in Chapter 4, Volume 2, while DMS quantum dots are discussed in Chapter 6, Volume 3. Electric-field control of magnetism in DMS has also revealed important opportunities in ferromagnetism metals, a discussed in Chapter 13 of Volume 2. The strong spin-orbit coupling in most DMS is responsible for the anomalous Hall effect discussed in Chapter 8, Volume 2.