Buckybowl tweezers are a relatively young research area closely associated with the development of non‐planar polycyclic aromatic systems and supramolecular chemistry. Since the appearance of the first prototypes in the early 2000s, the tweezers have undergone evolutionary changes. Nowadays they are able to effectively interact with fullerenes and the results opened up prospects for development in the field of sensing, nonlinear optics, and molecular switchers. In the present study, examples of corannulene‐based and other buckybowl tweezers for the recognition of C60 and C70 fullerenes were summarized and analyzed. The main structural components of the tweezers were also reviewed in detail and their role in the formation of complexes with fullerenes was evaluated. The revealed structural patterns should trigger the development of novel recognition systems and materials with a wide range of applications.