Atomically thin two-dimensional (2D) materials have attracted great interest due to their unique optoelectronic properties which are very different from their bulk counterparts. Most of the proof-of-concept devices, however, have been demonstrated using the scotch tape exfoliation method. The low yield thus limits the application of 2D materials and prevents them from meeting industry criteria. In order to fulfill potential roadmaps, it is essential to develop a reliable growth route and investigate the fundamental properties of as-grown materials in the atomically thin limit. Here, we have used molecular beam epitaxy (MBE) to grow atomically thin molybdenum diselenides (MoSe2) on GaAs(111)B. The as-grown nominal monolayer (ML) MoSe2 exhibits a direct bandgap and is highly oriented. Using polymer electrolyte gating, the ambipolar transport behavior of MBE-grown MoSe2 can be observed. The temperature-dependent transport can be explained by the 2D variable range hopping (2D-VRH) model, indicating that the transport is strongly limited by the nanostructures. The localization lengths derived from 2D-VRH can be modulated by electrolyte gating. We have further demonstrated the epitaxial growth of ML MoSe2 on h-BN/Rh(111) by MBE, revealing the electronic properties of the heterostructure using photoemission electron momentum microscopy (kPEEM). The valence band structures of ML MoSe2/h-BN/Rh(111) indicate that the valence band maximum(VBM) is located at the K point where the energy is 0.23 eV higher than that of the Gamma point, demonstrating the direct bandgap. Both h-BN and MoSe2 band structures have been preserved. The van der Waals (vdW) heterostructures grown using MBE thus provide a new material platform for future optoelectronic applications. Finally, we have extended the research to include gallium selenide (GaSe). Atomically thin GaSe has been predicted to have inverted topmost valence band structures at the Gamma point and can bring out novel, unique properties such as tunable magnetism. Here, we have systematically investigated the growth of atomically thin GaSe by MBE. The full valence band structures of nominal bilayer (BL) GaSe are revealed using kPEEM, highlighting the inverted topmost valence band near the Gamma point.