We give here an overview on our results on the large-area growth of 2D transition metal dichalcogenide semiconductors MoS2, MoSe2, WSe2 using chemical vapor deposition. The growth of MoS2 on sapphire occurs epitaxially with the crystalline orientation of the MoS2 film closely matching that of the sapphire substrate, resulting in a high-quality continuous film. The use of H2S results in more control over growth morphologies. WSe2 and MoSe2 have also been successfully grown using solid-state precursors. Room-temperature mobilities of all these materials exceed 10 cm(2)V(-1)s(-1). In contrast to MoS2, WSe2 and MoSe2 show ambipolar behavior.