Graphene's layered structure has opened new prospects for the exploration of properties of other monolayer-thick two-dimensional (2D) layered crystals. The emergence of these inorganic 2D atomic crystals beyond graphene promises a diverse spectrum of properties. For example, hexagonal-boron nitride (h-BN), a layered material closest in structure to graphene is an insulator, while niobium selenide (NbSe2), a transition metal dichalcogenide, is metallic, and monolayers of other transition metal dichalcogenides such as molybdenum disulfide (MoS2) and tungsten disulfide (WS2) are direct band gap semiconductors. The rich spectrum of properties exhibited by these 2D layered material systems can potentially be engineered on-demand and creates exciting prospects for using such systems in device applications ranging from electronics, photonics, energy harvesting, flexible electronics, transparent electrodes, and sensing. A review of the structure, properties, and the emerging device applications of these materials is presented in this paper. While the layered structure of these materials makes them amenable to mechanical exfoliation for quickly unveiling their novel properties and for fabricating proof-of-concept devices, an overview of the synthesis routes that can potentially enable scalable avenues for forming these 2D atomic crystals is also discussed.