This tutorial review covers the recent development in the synthesis and application of molecules and finite assemblies that are chiral owing to their curvature. A modified definition of inherent chirality is provided. Various classes of chiral concave molecules are presented including salphen complexes, cyclic amides, derivatives of sumanene, trioxatricornan or subphthalocyanine, cyclotriveratrylenes, homooxacalix[3]arenes, calixarenes, resorcinarenes, phthalocyanines, corannulenes and cavitands. Some of these bowl shaped compounds exhibit high inversion barriers, comparable with the stability of classical carbon chirality centres, while the others (e.g. hydrogen bonded assemblies) can only be detected by NMR. This review is focused on practical aspects of synthesis, resolution and applications in chiral recognition and asymmetric synthesis.