The past few years have witnessed a surge of activities in the study of graphene, a stable sheet comprised of just a single atomic layer of carbon atoms in a honeycomb lattice structure. Indeed, 2010 Nobel Physics Prize recognized two researchers for their pioneering contributions to this field. In this talk we will describe the development of the field and some of the reasons for the intense interest in this new material system, highlighting its unusual electronic dispersion and its distinctive mechanical and chemical properties. We will also discuss recent advances in the fabrication and investigation of other 2D atomic membranes. Examples include monolayer transition metal dichalcogenides and topological insulators.