Transition-metal dichalcogenides (TMDCs) are compounds consisting of a transition-metal M (Ti, Hf, Zr, V, Nb, Ta, Mo, W, Tc, Re, Pd, Pt) and chalcogen atoms X (S, Se, Te). There are approximately 60 compounds in the metal chalcogenide family, and two-thirds of them are in the form of layered structures where the in-plane bonds are strong (covalent), and the out-of-plane bonds are weak (van der Waals). This provides a means to mechanically or chemically thin (exfoliate) these materials down to a single atomic two-dimensional (2D) layer. While graphene, the 2D form of graphite, is metallic, the layered metal chalcogenides cover a wide range of electrical properties, from true metals (NbS2) and superconductors (TaS2) to semiconductors (MoS2) with a wide range of bandgaps and offsets. Multiple techniques are currently being developed to synthesize large-area monolayers, including alloys, and lateral and vertical heterostructures. The wide range of properties and the ability to tune them on an atomic scale has led to numerous applications in electronics, optoelectronics, sensors, and energy. This article provides an introduction to TMDCs, serving as a background for the articles in this issue of MRS Bulletin.