The fascinating properties of graphene, the first two-dimensional (2D) material, and the accompanying strong activity in the research community have sparked a renewed interest in related layered crystalline materials with unique electronic and optical properties. Their superb mechanical properties, optical transparency, direct band gap and large degree of electrostatic control due to their atomic scale thickness make them interesting inorganic nanosystems for a wide variety of applications. In this review we will present a short history of research in the synthesis, band properties and potential applications of 2D semiconductors with a particular emphasis on MoS2, the prototypical and best-studied material from this family. © 2014 Elsevier Ltd. All rights reserved.