The study of semiconductor interfaces is one of the most active and exciting areas of current semiconductor research. Because interfaces play a vital role in modern semiconductor technology (integrated circuits, heterojunction lasers, solar cells, infrared detectors, etc.), there is a strong incentive to understand interface properties at a fundamental level and advance existing technology thereby. At the same time, technological advances such as molecular beam epitaxy have paved the way for the fabrication of semiconductor heterojunctions and superlattices of novel design which exhibit unusual electronic, optical, and magnetic properties and offer unique opportunities for fundamental scientific research. A general perspective on this subject is offered treating such topics as the atomic and electronic structure of semiconductor surfaces and interfaces; oxidation and oxide layers; semiconductor heterojunctions and superlattices; rectifying metal-semiconductor contacts; and interface reactions. Recent progress is emphasized and some future directions are indicated. In addition, the role that large-scale scientific computation has played in furthering our theoretical understanding of semiconductor surfaces and interfaces is discussed. Finally, the nature of theoretical models, and the role they play in describing the physical world is considered.