Transition metal dichalcogenide (TMD) monolayers and heterostructures have emerged as a compelling class of materials with transformative properties that may be harnessed for novel device technologies. These materials are commonly fabricated by exfoliation of flakes from bulk crystals, but wafer-scale epitaxy of single-crystal films is required to advance the field. This article reviews the fundamental aspects of epitaxial growth of van der Waals-bonded crystals specific to TMD films. The structural and electronic properties of TMD crystals are initially described along with sources and methods used for vapor phase deposition. Issues specific to TMD epitaxy are critically reviewed, including substrate properties and film-substrate orientation and bonding. The current status of TMD epitaxy on different substrate types is discussed along with characterization techniques for large-areaepitaxial films. Future directions are proposed, including developments in substrates, in situ and full-wafer characterization techniques, and heterostructure growth.