The generally strong chemical interactions between semiconductors and metals introduce additional complexities in the experimental characterization and modelling of epitaxial growth. This article reviews the relevant epitaxial parameters and growth modes in relation to what is known to occur on semiconductors. A salient property of some metals and semimetals is their tendency to form covalent bonds, whose directionality strongly influences the epitaxial relationship between substrate and overgrowth. Both the substrate orientation and, for the binary semiconductors, the stoichiometry of the substrate, strongly influence the epitaxial relationships. Representative examples of the different growth modes are discussed in relation to interfacial bonding, with emphasis on the growth differences between Al, a reactive metal, and Ag, a nonreactive metal on GaAs. The latter part of the article discusses some of the outstanding issues of the epitaxy of metals on semiconductors and possible approaches to their solution.