Our recent studies have focused on the epitaxial growth of WSe2 and WS2 monolayer films and heterostructures using metal hexacarbonyl and hydride chalcogen precursors on substrates including sapphire and hexagonal boron nitride (hBN). A multi-step precursor modulation growth method was developed to independently control nucleation density and the lateral growth rate of WSe2 and WS2 monolayer domains on the substrate. This approach also enables measurement of W-species surface diffusivity and domain growth rate as a function of growth conditions providing insight into the fundamental mechanisms of monolayer growth. Using this approach, coalesced monolayer and few-layer TMD films were obtained on sapphire substrates up to 2” in diameter at growth rates on the order of ~ 1 monolayer/hour. In-plane X-ray diffraction demonstrates that the films are epitaxially oriented with respect to the sapphire resulting from a merging of an equal mixture of 0o and 60o oriented domains. WSe2 also grows epitaxially on hBN single crystal flakes but in this case the domains exhibit a predominant direction resulting in a reduced density of anti-phase boundaries. Applications and challenges of this approach in the growth of 2D heterostructures will also be discussed.