The properties of semiconductor superlattices--solid-state structures in which there exists, in addition to the periodic potential of the crystal lattice, a one-dimensional potential whose period is much longer than the lattice constant—are studied. The existence of the superlattice potential substantially alters the energy spectrum, as a result of which superlattices have a number of interesting properties which ordinary semiconductors do not have. Superlattices offer a unique possibility for altering their band structure practically arbitrarily. The characteristic features of the luminescence of superlattices (tunability of the emitted wavelengths, the excitonic nature of the radiation up to room temperature, strong suppression of impurity trapping, femtosecond kinetics, etc.) are being exploited to develop a new generation of light-emitting devices. The acoustic properties of superlattices are characterized by the existence of selective reflection of phonons. Semiconductor superlattices are characterized by substantially nonlinear transport properties, owing to the presence of very narrow minibands in their energy spectrum.