Density functional theory with the B3LYP hybrid functional has been used to study the mechanisms for dioxygen activation by four families of mononuclear non-heme iron enzymes: alpha-ketoacid-dependent dioxygenases, tetrahydrobiopterin-dependent hydroxylases, extradiol dioxygenases, and Rieske dioxygenases. These enzymes have a common active site with a ferrous ion coordinated to two histidines and one carboxylate group (aspartate or glutamate). In contrast to the heme case, this type of weak field environment always leads to a high-spin ground state. With the exception of the Rieske dioxygenases, which have an electron source outside the active site, the dioxygen activation process passes through the formation of a bridging-peroxide species, which then undergoes O-O bond cleavage finally leading to the four electron reduction of O(2). In the case of tetrahydrobiopterin- and alpha-ketoacid-dependent enzymes, the O-O heterolysis yields a high-valent iron-oxo species, which is capable of performing a two-electron oxidation chemistry on various organic substrates. For the other two families of enzymes (extradiol dioxygenases and Rieske dioxygenases) the substrate oxidation and the O-O bond cleavage are found to be coupled. In the extradiol dioxygenases the product of the O-O bond cleavage is a ferric iron with an oxy-substrate with a mixture of radical and anionic character, which is essential for the selectivity of the catechol cleavage.