During recent years diluted magnetic semiconductors based on III—V compounds have been of considerable interest. In this respect we review the basic properties of these materials, which are nearly exclusively Mn-based systems, such as GaMnAs, InMnAs, GaMnSb, and GaN:Mn. We discuss the nature of Mn impurity. Different Mn centers are considered and experimental pieces of evidence suggesting the dominating role of Mn (d5 ) configuration are given. Then we analyze s, p — d exchange, together with resulting magnetooptical properties (in particular absorption edge slitting for heavily p-type GaMnAs). The coupling between Mn ions (d— d exchange) and ferromagnetic ordering observed in InMnAs and GaMnAs is the next subject. Some mechanisms responsible for this ordering are presented. Finally we discuss transport properties and some selected problems of quantum structures based on III—V diluted magnetic semiconductors.