This paper provides an overview of research developments toward nanometer-scale electronic switching devices for use in building ultra-densely integrated electronic computers. Specifically, two classes of alternatives to the field-effect transistor are considered: (1) quantum-effect and single-electron solid-state devices and (2) molecular electronic devices. A taxonomy of devices in each class is provided, operational principles are described and compared for the various types of devices, and the literature about each is surveyed. This information is presented in nonmathematical terms intended for a general, technically interested readership.