Over the last decade, graphene research has developed into a large and multi-faceted field concerned with the synthesis, structure, properties, and applications of various ultrathin sheet-like carbon forms. This article presents a historical perspective on ultrathin carbons, and on the traditional role of the “graphene layer” as a conceptual model for describing crystalline polymorphs in sp < sup > 2 -based carbon materials. Bulk carbons can often be usefully modelled as physical assemblies of distinct graphene layers whose length, curvature, packing, and orientation determine carbon properties and their observed anisotropy. The article then gives a brief perspective on the emerging subfield of graphene research that uses nanosheets as physical building blocks to assemble new material architectures. In analogy with macroscopic sheets of paper or fabric, graphene nanosheets can be manipulated by stacking, wrapping, folding, wrinkling, or crumpling, to make novel carbons not accessible through traditional routes based on molecular or solid-state precursors. These include aerogels, crumpled particles, encapsulation sacks, and a variety of engineered films structures that can be planar or microtextured. While much work has been done in this graphene subfield, important research opportunities remain. Among these are the creation of hybrid structures involving graphene nanosheets systematically combined with other substances to form graphene-molecular hybrids, graphene-nanoparticle hybrids (2D-0D), graphene-nanofiber hybrids (2D-1D), and nanosheet heterostructures (2D-2D).