A review is given of advances in the field of carrier-controlled ferromagnetism in Mn-based diluted magnetic semiconductors and their nanostructures. Experimental results for III-V materials, where the Mn atoms introduce both spins and holes, are compared to the case of II-VI compounds, in which the Curie temperatures T_C above 1 K have been observed for the uniformly and modulation-doped p-type structures but not in the case of n-type films. The experiments demonstrating the tunability of T_C

more »

... y light and electric field are presented. The tailoring of domain structures and magnetic anisotropy by strain engineering and confinement is discussed emphasizing the role of the spin-orbit coupling in the valence band. The question of designing modulated magnetic structures in low dimensional semiconductor systems is addressed. Recent progress in search for semiconductors with T_C above room temperature is presented.