State-of-the-art in quantum-chemical research on endohedral fullerenes is considered. Separate chapters are devoted to complexes with noble gases, main group elements, and methals and their nitrides. The structures and the mechanisms of formation and decomposition of these compound sare highlighted. Applicability of various quantum-chemical methods for endohedral fullerene complexes is discussed. Problems associated with the use of the ROHF and UHF methods are revealed. The DFT method with hybrid functionals and effective core potentials for heavy atoms is shown to hold the greatest promise.