Recent advances in the development of atomically thin layers of van der Waals bonded solids have opened up new possibilities for the exploration of 2D physics as well as for materials for applications. Among them, semiconductor transition metal dichalcogenides, MX 2 (M = Mo, W; X = S, Se), have bandgaps in the near-infrared to the visible region, in contrast to the zero bandgap of graphene. In the monolayer limit, these materials have been shown to possess direct bandgaps, a property well suited for photonics and optoelectronics applications. Here, we review the electronic and optical properties and the recent progress in applications of 2D semiconductor transition metal dichalcogenides with emphasis on strong excitonic effects, and spin- and valley-dependent properties. © 2016 Macmillan Publishers Limited. All rights reserved.