Abstract Quantum chemical studies by the author and co-workers on dioxygen activation and methane hydroxylation by diiron and dicopper enzyme species as well as related metal–oxo species are reviewed. The activation of the O–O bond of dioxygen at the mono- and dimetal sites of metalloenzymes is an essential process in the initial catalytic stages of naturally occurring oxygenation reactions. A way of orbital thinking about dioxygen activation at diiron and dicopper enzymes is developed at the extended Hückel level of theory. Two different reaction pathways that lead from dimetal peroxo complexes with µ-η1:η1-O2 and µ-η2:η2-O2 modes to the corresponding dioxo complexes are discussed in detail. In considering the mechanism of methane hydroxylation, special attention to FeO+-mediated methane hydroxylation that occurs under ion cyclotron resonance (ICR) conditions is given. Mechanistic aspects about methane hydroxylation by the bare transition-metal oxide ions ScO+, TiO+, VO+, CrO+, MnO+, FeO+, CoO+, NiO+, and CuO+ are systematically analyzed on the basis of density functional theory (DFT) calculations. An important feature in the reaction is the spin crossover between the high-spin and low-spin potential energy surfaces in particular in the C–H activation process. The spin inversion from the high-spin state to the low-spin state effectively decreases the barrier height of C–H activation. Another feature in the reaction is that no radical species is involved in the course of the hydroxylation because the methyl species formed as a result of the C–H bond cleavage can directly coordinate to the metal active site. The coupling of the OH and CH3 ligands occurs to produce methanol at the metal active center. The reaction profiles obtained from DFT calculations are similar to those of the Gif chemistry proposed by D. H. R. Barton, in particular the involvement of the HO–M–CH3 species as an intermediate in the hydroxylation of methane. The nonradical mechanism is extended to methane hydroxylation by the diiron and dicopper species of methane monooxygenase (MMO). This mechanism is possible when the metal active center is coordinatively unsaturated to have a space for the coordination of the OH and CH3 groups as ligands. Although compelling discussion to support the involvement of oxygen- and carbon-centered radicals is provided, the nonradical mechanism still seems to be applicable for methane hydroxylation from the viewpoint of reaction selectivity. Kinetic isotope effects (KIEs) in the C–H activation process by the bare FeO+ complex and diiron and dicopper enzyme models are compared with respect to the radical and nonradical mechanisms by using transition state theory.