Buckyballs Juan L. Delgado, Salvatore Filippone, Francesco Giacalone, Mª Ángeles Herranz, Beatriz Illescas, Emilio M. Pérez, and Nazario Martín* * Departamento de Química Orgánica, Facultad de Química, Universidad Com- plutense, E-28040 Madrid, Spain. IMDEA-Nanosciece, Campus de Cantoblanco, E-28049 Madrid, Spain. E-mail:nazmar@quim.ucm.es http://www.ucm.es/info/fullerene Abstract Buckyballs represent a new and fascinating molecular allotropic form of carbon that has received a lot of attention by the chemical community during the last two decades. This unabbated interest on this singular family of highly strained carbon spheres has allowed establishing the fundamental chemical reactivity of these carbon cages and, therefore, a huge variety of fullerene derivatives involving [60] and [70]fullerenes, higher fullerenes and endohedral fullerenes have been prepared. Much less is known, however, on the chemistry of the uncommon non-IPR fullerenes which currently represent a scientific curiosity and which could pave the way to a new universe of new fullerenes. In this review on buckyballs we have mainly focused on the most recent and novelty covalent chemistry of fullerenes involving metal catalysis and asymmetric synthesis, as well as on some of the most significant advances in supramolecular chemistry, namely H-bonded fullerene assemblies and the search for efficient concave receptors for the convex surface of fullerenes. Furthermore, we have also described the recent advances of the macromolecular chemistry of fullerenes, that is, those polymer molecules endowed with fullerenes which have been classified according to their chemical structures. The content of this review is completed with the study of endohedral fullerenes, a new family of fullerenes in which the carbon cage of the fullerene contain a metal, molecule or metal complex in the inner cavity. The presence of these species affords new fullerenes with complete different properties and chemical reactivity, thus opening a new avenue in which a more precise control on the photophysical and redox properties of fullerenes is possible. The use of fullerenes for organic electronics, namely in photovoltaic applications and molecular wires, complement the study and highlight the interest of these carbon allotropes for realistic practical applications. We have pointed out the so-called non-IPR fullerenes - those that do not follow the isolated pentagon rule – as the most intriguing class of fullerenes which, up to now, have only shown the tip of the huge iceberg behind the former examples reported in the literature. The number of possible non-IPR carbon cages is almost infinite and the next future will show us wether they will become a reality.