The discovery of graphene has created a great sensation in chemistry, physics, materials science, and related areas. The unusual properties of graphene have aroused interest in other layered materials, such as molybdenum sulfide and boron nitride. In the last few years, single- as well as few-layer as well as chalcogenides and other inorganic materials have been prepared and characterized by a variety of methods. These materials possess interesting properties, and some have potential applications. This Review provides an up-to-date account of these emerging two-dimensional nanomaterials. Not only are the synthesis and characterization covered, but also important aspects such as spectroscopic and optical properties, magnetic and electrical properties, as well as applications. Salient features of the composites formed from the layered inorganic structures with graphene and polymers are presented along with a brief description of borocarbonitrides.