Homolytic bond dissociation enthalpies (BDEs) for C-H bonds in substituted methanes, C-O bonds in peroxyl radicals, and for O-H bonds in hydroperoxides have been calculated using density functional theory at the B3LYP/6-31G(d,p) and B3LYP/6-311+G(2df,2p) levels of theory, and using ab initio theory at the G2MS level. Ionization energies (IEs) of substituted methyl radicals and electron affinities (EAs) of peroxyl radicals have been calculated using the same methods. It is found that the B3LYP method is not generally reliable for prediction of absolute BDEs. However, this method works well for prediction of substituent effects on BDEs and for prediction of Ifs and EAs. The deviations from experimental values are generally within 2-3 kcal/mel. The accuracy of the G2MS method is in general slightly better, and it is also capable of predicting accurate absolute BDEs. The stability of alkyl radicals is largely affected by substituents. This gives rise to large substituent effects on the C-H BDE in substituted methanes and the C-O BDE in peroxyl radicals. However, in the latter case the relative stabilization of the peroxyl radical is also of great importance for determining the BDE, In particular, electron-donating substituents have large stabilizing effects on peroxyl radicals. The substituent effects on the O-H bond in hydroperoxides are relatively small and largely determined by internal hydrogen bonding. There are relatively large substituent effects on the IE of alkyl radicals and the EA of peroxyl radicals. For some of the alkyl radicals with electron-withdrawing substituents, the ionization process leads to a considerable rearrangement of the nuclear configuration. In particular, three-membered ring systems are in several instances favored energetically over primary carbocations.