The quantum confinement of electrons and holes in low-dimensional semiconductor structures strongly influences the properties of ''quantum wires and dots'' and therefore has an important impact on the performance of high-speed electron and optoelectronic devices. The fabrication of such structures using. for example, molecular beam epitaxy and metal-or-organic vapor phase epitaxy, their characterization, and their use in heterojunctions, quantum wells, and high electron mobility transistors are reviewed.