Fullerene chemistry has become a very active research field in the two last decades, largely because of the exceptional properties of the C60 molecule and the variety of fullerene derivatives that appear to be possible. In this review, a general analysis of fullerene C60 reactivity is performed. The principal methods for the covalent modification of this fascinating carbon cage are presented. The prospects of using fullerene derivatives as medicinal drugs and photoactive materials in light converting devices are demonstrated.