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 detail. 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. Furthermore, chemical trends are discussed and lead to the prediction of semiconductor systems with T_C that may exceed room temperature. This expectation is being confirmed by recent findings. Results for materials containing magnetic ions other than Mn are also presented emphasizing that the double exchange involving hopping through d states may operate in those systems.