  The current status and prospects of research on ferromagnetism in
semiconductors are reviewed. The question of the origin of ferromagnetism in
europium chalcogenides, chromium spinels and, particularly, in diluted magnetic
semiconductors is addressed. The nature of electronic states derived from 3d of
magnetic impurities is discussed in some details. Results of a quantitative
comparison between experimental and theoretical results, notably for Mn-based
III-V and II-VI compounds, are presented. This comparison demonstrates that the
current theory of the exchange interactions mediated by holes in the valence
band describes correctly the values of Curie temperatures T_C magnetic
anisotropy, domain structure, and magnetic circular dichroism. On this basis,
chemical trends are examined and show to lead to the prediction of
semiconductor systems with T_C that may exceed room temperature, an expectation
that are being confirmed by recent findings. Results for materials containing
magnetic ions other than Mn are also presented emphasizing that the double
exchange involving hoping through d states may operate in those systems.
