This article reviews the present status of superradiance in atoms and molecules. The introductory section describes the important physical properties of superradiant emission, and presents the important experimental features. A simple theoretical formulation, based on the coupled Maxwell-Schrödinger equations, is described. Simple expressions for observable output parameters are given, valid in experimentally relevant regimes. These results are compared with superradiance experiments performed at a wide range of wavelengths in numerous laboratories since 1973. While the principal features of superradiance are generally agreed upon, details of the initiation of the radiation process and of the observed ringing are still under study.