Unprecedented reactions involving the highly reactive double bonds of the fullerene sphere undergoing cobalt-catalyzed [2+2+1], thermally induced [2+2], and ene cycloadditions have been researched in a systematic way. In addition, the highly efficient retro-cycloaddition processes of fulleropyrrolidines (Prato cycloadducts) and fulleroisoxazolines are also discussed in detail. These new reactions in fullerene chemistry reveal that the unique scenario presented by the convex and highly reactive surface in fullerenes has not yet been appropriately exploited, and that it is still possible to create new and fascinating structures.