Buckybowls, bowl‐shaped polycyclic aromatic hydrocarbons structurally related to fullerenes, represent a class of hydrocarbons with unique properties and a potential for application as novel materials. This review outlines the development of the practical preparations of buckybowls, starting with the original synthesis of corannulene achieved in 1966. A particular attention is paid to the last decade developments which include construction of large, highly nonplanar molecular networks (molecular clips and tweezers) capable of binding guest molecules of various sizes and shapes. In particular, such molecular clips were proven to form stable supramolecular complexes with fullerenes C60 and C70, both in solution and in the solid state.