Buckminsterfullerene (C60) is a very reactive molecule, which easily undergoes a large variety of chemical transformations. Exohedral addition reactions to the fullerene cage are the most important methods for the derivatization of C60. During the first five years of fullerene chemistry a large number of additions to C60, such as nucleophilic- and radical additions, cycloadditions, hydrogenations, transition metal complex formations, oxygenations and halogenations, have been investigated. The basic characteristics of the reactivity as well as of the regiochemistry of additions to the fullerene cage have been revealed and are predominantly based on the strained spherical structure of this all-carbon molecule.