The growth by molecular-beam epitaxy of high-quality epitaxial layers of GaAs, AlGaAs, and InGaAs on GaAs substrates oriented normal to the [111] direction is reported. The (111)B surface of GaAs is found, in contrast to the (001) surface, to be extremely fragile after the desorption of its oxide. Surface roughening occurs within seconds of oxide desorption unless growth is initiated promptly. Reflection high-energy electron diffraction studies also reveal several structural transformations occurring on the surface of the substrate. The reconstructions are sensitive to the temperature and to the arsenic flux. Temperature and flux ranges leading to two-dimensional, monolayer growth are delineated, and this information is used to grow superlattices and quantum wells with smooth interfaces. Both unstrained lattice-matched and strained pseudomorphic layers have been grown.