The idea of onion-like carbon nanostructures has not been long to emerge, after the discovery of Buckminsterfullerene, C60, which has 60 carbon atoms forming a truncated-icosahedral structure with 12 pentagonal rings and 20 hexagonal rings. These types of structures are considered as new allotropes of carbon. Carbon-onions are endohedrally fullerene doped systems; the smallest ball is located in the most inner hole, and the cover gets bigger and bigger. The new carbon allotropes, the fullerenes, are closed-cage carbon molecules with three-coordinate carbon atoms tiling spherical or nearly-spherical surfaces. Carbon-based fullerenes were discovered in 1985. The electron irradiation experiments by Ugarte encouraged scientists to explore alternative routes for the formation of carbon anions and the simplest of which was the heat treatment of preformed carbon nanostructures. The bulk modulus of fullerenes and onions were calculated as a function of the diameter as well as the number of shells at various temperatures, to evaluate their hardness.