Nearly 30 years after their discovery, fullerenes, the third allotrope of carbon, remain attracting the interest of many researchers worldwide due their unique properties and applications in wide ranging fields from material science to medicine. Nowadays, the design and synthesis of fullerenes receptors is a very attractive field of research. Besides their great importance in the development of new materials in nanotechnology and nanoscience, fullerene receptors also could be crucial for separation of fullerenes. A promising strategy to design new molecular receptors for fullerenes is using the concave-convex complementarity. Nevertheless, the examples of concave fullerene receptors are relatively scarce since curved molecules are not always an easy synthetic target due their tensioned structures. In this context, bowl-shaped polycyclic aromatic hydrocarbons, commonly known as buckybowls or fullerene fragments seem very attractive because several buckybowls have been synthetized in recent years and their concave surface can fit adequately to the convex surface of fullerenes through concave-convex “ball-and-socket” pi-pi interactions. In 2007, Sygula and co-workers introduced a novel type of molecular tweezers (a buckycatcher, C60H28) with buckybowl pincers that have attracted a substantial interest of researchers due their ideal architecture for recognizing fullerenes and their potential future applications, in particular as stationary phases in liquid chromatography for the separation of fullerenes or as buckycatcher-fullerene complexes in photovoltaic devices (A. Sygula et al. J. Am. Chem. Soc. 2007, 129, 3842). Despite their great interest, the number of theoretical studies of concave-convex pi-pi interactions between buckybowls and fullerenes are limited due to the recent discovery of these structures, to their large size and, especially, to the fact that until a few years ago there were no satisfactory options for the precise calculation of the non-covalent interactions between large molecules. For that reason, the goal of this doctoral thesis is to carry out an exhaustive theoretical study of the concave-convex pi-pi interactions between buckybowls and fullerenes in order to get a better understanding of the supramolecular systems existing and guiding the design of new systems more effective and/or selective. The methodology of quantum chemistry will be used for this purpose. This methodology has proved to be a powerful tool for understanding phenomena of many kinds. It can provide valuable information, both interpretative, since it can provide a better knowledge of the intimate properties of matter, and predictive, since results can be an important aid for designing appropriate molecules that make use of interactions involving these species.