Molecule of fullerene, having a spherical or ellipsoidal shape, is made of rings consisting of five or six carbon atoms, combined with conjugated pi bonds. Delocalization of pi electrons in the molecule of fullerene makes it easy to scavenge free radicals. But, despite being the effective antioxidants and radical scavengers fullerenes may be prooxidants by reactive oxygen species generation. Mammalian cells consist mainly of water (about 70%). Thus, the radical and non-radical products of water radiolysis are the basic sources of radiation damage to biomolecules. Reactive oxygen species, such as hydroxyl (HO*) and superoxide (O2-*) radicals and hydrogen peroxide (H2O2), are responsible for radiation-induced damage in aerated systems. Free radical mechanism of radiation damage suggests that scavengers of free radicals should protect cellular structures against damage. Electron donor compounds should also exhibit protective properties towards oxidized functional groups by reducing them. However, the electron transfer from fullerene to oxygen may generate superoxide radical. The shape of fullerenes allows them to act as carriers of radioactive atoms of isotopes used in the therapy and medical diagnostics. Fullerenes and their derivatives due to its properties are new promising chemicals for application in radiobiology. Fullerenes may be radioprotectors, radiosensitizer or auxiliary compounds in diagnostic imaging. What they are depends on the experimental system used.