The discovery of fullerenes has opened novel opportunities for radical chemistry. The fullerenyl radical adducts formed via addition of atoms or free radicals to fullerenes have no analogs in organic chemistry. Thus, the elucidation of the characteristic features of fullerenyl radicals and their reactivity by EPR spectroscopy is of fundamental importance. Isolation of the products from homolytic reactions of fullerenes in bulk amounts opens the door to large-scale preparation of new organic and organoelement derivatives of C60, including biologically active ones. Radical reactions of fullerenes find wide application in the synthesis of fullerene-containing polymers with valuable photophysical characteristics. Ferromagnetism of the complex of C60 with tetra(dimethylamino)ethylene lends impetus to a search for novel methods for preparation of biradicals, with one unpaired electron located on the fullerene cage and the other retained by the addend. This book covers the results of studies on homolytic reactions of fullerenes, the structures and reactivities of fullerenyl radicals performed by EPR, quantum-chemical, and other methods. Examples of the application of radical reactions of fullerenes in the synthesis and typical methods for their investigation are given.