We all are very familiar with graphene and carbon nanotubes and their extraordinary electronic and mechanical properties. Both materials are composed of sp2 carbon atoms; their structures look very similar locally but exhibit different properties due to the way their atoms are arranged in 3D space. In this talk, first: I will explain how graphene, carbon nanotubes and fullerenes can be seen under a unified concept, the concept of curvature, which can be applied to any other 2D material. Under this concept, I will explain how different structures can be proposed at different scales and levels of complexity. Second, I will show the richness of 2D semiconductors such as transition metal dichalcogenides (TMDs); I will focus on their amazing non-linear optical properties. Finally, the quantum single photon emission of a 2D insulating material known as hexagonal boron nitride (h-BN) will be explained and what the challenges are for its applications.