[en] Using density functional calculations over the last decade led to considerable progress in understanding the mechanism of olefin epoxidation with Ti, V, Mo, W, and Re peroxy complexes. According to calculations, the reaction occurs by direct electrophilic transfer of one of the atoms of the peroxy group to the olefin. The alternative stepwise mechanism, which has been discussed for a long time and suggested the formation of a metallocyclic intermediate, is characterized by higher activation barriers than direct transfer. The electrophilic character of the direct transfer of oxygen was interpreted at the level of molecular orbital analysis as interaction between the HOMO of the olefin π(C-C) and the LUMO of the peroxy group σ*(O-O). The factors determining the activity of various metal complexes in epoxidation were examined in relation to the ligand environment and the structure of the peroxy group