This review briefly describes a state of research on the effect of fullerenes and carbon nanotubes (CNTs) on a durability of various polymer composite materials under extreme conditions. Fullerenes C60, C70, fullerene soot and CNTs integrated into the polymer matrix effectively prevent both thermal and thermo-oxidative degradation, as well as photo-oxidation processes. The stabilization mechanism of the carbon nanocompounds (CNC) is likewise and consists of the substantial end-capping termination of oxidation destructive chains on the nanocarbon skeleton. At that, the data array unequivocally indicates the predominant addition of carbon-centered alkyl radicals. Various polymer composite materials based on polyolefins, polyacrylates, polyamides, polycarbonates, elastomers are involved into the consideration. The approaches described are mostly aimed to increase the level of stabilizing activity of the polymer composites using different combinations of nanocarbon additives. The optimal dosage of CNC and interfacial compatibility between the polymer and fillers can significantly increase the heat resistance of the composites. The replacement of carbon atoms in the fullerene molecule with heteroatoms can also change its electronic properties and improve the antiradical and antioxidant activity. Areas for the effective use of fullerene C60 in aqueous media can be significantly expanded by modification with hydrophilic polymers. Thus, the performance of CNC integrated in the polymer composites is similar with those for strong synthetic stabilizers. CNC have good prospects for real industrial applications.