Quasicrystals are fascinating intermetallic compounds composed of two or more elements. They differ from conventional crystals in that they possess long-range order, but no translational symmetry--that is, they are aperiodic. Much effort has been expended on identifying routes towards exploiting and exploring the properties of such systems due to their aperiodic nature. One such route is concerned with the deposition of thin films, particularly of metals, to investigate how their growth progresses in this inherently frustrated scenario. This topical review will examine the various epitaxial relationships observed in quasicrystal research with particular emphasis on single-element metallic films deposited under ultrahigh-vacuum conditions.