In the past two decades, quantum chemistry has become an indispensable tool for the reliable interpretation of experimental measurements of a wide range of molecular properties of fullerene and its derivatives. Among the modern quantum‐chemical methods of analysis, preference is given to the density functional theory. This review describes the computational studies that demonstrate rather comprehensively the prospects of quantum‐chemical calculations in many fields of the chemistry of fullerene and its derivatives, such as geometric parameters, stability of structures, molecular spectroscopic properties, electronic structures, the nature of bonds, thermochemistry, and simulation of the kinetics and mechanism of processes. The review focuses on the most typical cycloaddition reactions such as Diels–Alder, Prato and Bingel–Hirsch reactions. The general trends of scientific studies in this area are also discussed and a wide range of references is provided where the readers can find technical details of computational approaches that may be of interest for them.
