Here we review fullerenes biological effects focusing on their antioxidant and anti-ageing action. A scope of various poisonous and healing properties reported in literature for fullerene and its derivatives is analyzed. The review begins with the history of fullerenes discovery and their main properties. Then we focus on the longevity and antioxidant action, including the confrontation of available experimental data and theoretical modeling of buckminsterfullerene C60. Special attention is given to our hypothesis concerning the possibility of fullerenes to act as mitochondria protonophore and various simulations of the transport of C60 and its hydroxylated and other derivatives through lipid bilayer membranes, which can account for scavenging capacity of fullerenes for reactive oxygen species and their acting as mild mitochondrial respiration uncouplers. Extension of the theoretical modeling to the mitochondria membranes and implications on the real biological systems is analyzed. Finally, we focus on the toxicity evaluation and current therapeutic usage of fullerenes. The review contains a comprehensive discussion of both papers published by 2016 and our own research results.