Recent years have witnessed extensive research aimed at developing functional, tetrahedrally coordinated ferromagnetic semiconductors that could combine the resources of semiconductor quantum structures and ferromagnetic materials systems and thus lay the foundation for semiconductor spintronics. Spin-injection capabilities and tunability of magnetization by light and electric field in Mn-based III–V and II–VI diluted magnetic semiconductors are examples of noteworthy accomplishments. This article reviews the present understanding of carrier-controlled ferromagnetism in these compounds with a focus on mechanisms determining Curie temperatures and accounting for magnetic anisotropy and spin stiffness as a function of carrier density, strain, and confinement. Materials issues encountered in the search for semiconductors with a Curie point above room temperature are addressed, emphasizing the question of solubility limits and self-compensation that can lead to precipitates and point defects. Prospects associated with compounds containing magnetic ions other than Mn are presented.