In nature there are numerous layered compounds, some of which could be curved so as to form fascinating nanoshapes with novel properties. Graphite is at present the main example of a very flexible layered structure, which is able to form cylinders (nanotubes) and cages (fullerenes), but there are others. While fullerenes possess positive curvature due to pentagonal rings of carbon, there are other structures which could include heptagonal or higher membered rings. In fact, fullerenes and nanotubes could display negative curvature, thus forming nanomaterials possessing unexpected electronic and mechanical properties. The effect of curvature in other nano–architectures, such as in boron nitride and metal dichalcogenides, is also discussed in this account. Electron irradiation is a tool able to increase the structural complexity of layered materials. In this context, we describe the coalescence of carbon nanotubes and C60 molecules. The latter results now open up an alternative approach to producing and manipulating novel nanomaterials in the twenty–first century.