Fullerenes are molecules made of carbon and they have an extraordinary ability to soak up free radicals. So much so, they were dubbed the radical sponge. Since then, numerous studies, patents and papers have demonstrated the effectiveness of fullerenes, also known as C60, as the enemy of free radicals. Mitsubishi has a company in Japan, Vitamin C60, dedicated to using C60 in skincare.
Zelens, a UK company, used C60 in its product line until it was forced controversy in the media to stop. Consumer Reports magazine quoted the Nobel prize-winning discoverer of it saying he wouldn't put it in a skincream - although the quote was slightly ambiguous and it wasn't clear whether he merely disdained cosmetic creams or actually did think it might be unsafe. Anyway, it caused a furore and Zelens promptly reformulated its products without C60.
So is fullerenes safe in a skincare product, or not? Probably not. A University of Oregon study concluded that it causes oxidative stress. Mind you, the tests were conducted on zebrafish. And there have been studies on mice that concluded that fullerenes were not toxic. However, other reports, show that when exposed to sunlight, C60 becomes toxic; safe C60 is essentially "pristine and dark". Another test on bass (I'm not quite sure what it is about fish and fullerenes) resulted in lipid peroxidation of the brain. Friends of the Earth says "even low levels of exposure to fullerenes have been shown to damage human liver cells".