Mixed-valence manganese oxides (R1-x Ax)MnO3 (R=rare-earth cation, A=alkali or alkaline earth cation), with a structure similar to that of perovskite CaTiO3, exhibit a rich variety of crystallographic, electronic and magnetic phases. Historically they led to the formulation of new physical concepts such as double exchange and the Jahn-Teller polaron. More recent work on thin films has revealed new phenomena, including colossal magnetoresistance near the Curie temperature, dense granular magnetoresistance and optically-induced magnetic phase transitions. This review gives an account of the literature on mixed-valence manganites, placing new results in the context of established knowledge of these materials, and other magnetic semiconductors. Issues addressed include the nature of the electronic ground states, the metal-insulator transition as a function of temperature, pressure and applied magnetic field, the electronic transport mechanisms, dielectric and magnetic polaron formation, magnetic localization, the role of cation disorder and the Jahn-Teller effect. Sample preparation, and the properties of related ferromagnetic oxides are also discussed.