This article reviews the major physico-chemical aspects of molecular beam epitaxy (MBE), especially as applied to the deposition of thin epitaxial films of 111-V compound and alloy semiconductors. The experimental requirements to achieve the necessary levels of control, purity and uniformity are described first to establish the basic features of the technique. This is followed by a rather detailed treatment of the growth process, including thermodynamic considerations, surface reaction kinetics and film growth dynamics. Because MBE provides a unique means of preparing clean surfaces having controlled stoichiometry and reconstruction, the evaluation of their crystallographic and electronic structure is dealt with at some length.The structure and composition of semiconductor-semiconductor interfaces, together with the formation of quantum wells and periodic superlattices, are topics of increasing importance and as such also receive considerable attention. Dopant incorporation is dealt with rather more briefly by reference to specific examples and finally some mention is made of materials other than 111-V semiconductors which have been prepared by MBE.