The influence of electron attachment on the stability of the mono- and dihydrogenated buckminsterfullerene C60 was studied using density functional theory and semiempirical molecular orbital techniques. We have also assessed the reliability of computationally accessible methods that are important for investigating the reactivity of graphenic species and surfaces in general. The B3LYP and M06L functionals with the 6-311+G(d,p) basis set and MNDO/c are found to be the best methods for describing the electron affinities of C60 and C60H2. It is shown that simple frontier molecular orbital analyses at both the AM1 and B3LYP/6-31G(d) levels are useful for predicting the most favourable position of protonation of C60H−, that is, formation of the kinetically controlled product 1,9-dihydrofullerene, which is also the thermodynamically controlled product, in agreement with experimental and previous theoretical studies. We have shown that reduction of exo- and endo-C60H makes them more stable in contrast to the reduction of the exo,exo-1,9-C60H2, reduced forms of which decompose more readily, in agreement with experimental electrochemical studies. However, most other dihydrofullerenes are stabilized by reduction and the regioselectivity of addition is predicted to decrease as the less stable isomers are stabilized more by the addition of electrons than the two most stable ones (1,9 and 1,7).