The nature of the bonding in model complexes of di-copper metalloenzymes has been analyzed by means of the electronic localization function (ELF) and by the quantum theory of atoms in molecules (QTAIM). The constrained space orbital variations (CSOV) approach has also been used. Density functional theory (DFT) and CASSCF calculations have been carried out on several models of tyrosinase such as the sole Cu2O22+ central core, the Cu2O2(NH3)62+ complex and the Cu2O2(Imidazol)62+ complex. The influence on the central Cu(2)O(2) moiety of both levels of calculation and ligand environment have been discussed. The distinct bonding modes have been characterized for the two major known structures: [Cu(2)(mu-eta(2): eta(2)-O(2))](2+) and [Cu(2)(mu-O(2))](2+). Particular attention has been given to the analysis of the O-O and Cu-O bonds and the nature of the bonding modes has also been analyzed in terms of mesomeric structures. The ELF topological approach shows a significant conservation of the topology between the DFT and CASSCF approaches. Particularly, three-center Cu-O-Cu bonds are observed when the ligands are attached to the central core. At the DFT level, the importance of self interaction effects are emphasized. Although, the DFT approach does not appear to be suitable for the computation of the electronic structure of the isolated Cu(2)O(2) central core, competitive self interaction mechanisms lead to an imperfect but acceptable model when using imidazol ligands. Our results confirm to a certain extent the observations of [M.F. Rode, H.J. Werner, Theoretical Chemistry Accounts 4-5 (2005) 247.] who found a qualitative agreement between B3LYP and localized MRCI calculations when dealing with the Cu(2)O(2) central core with six ammonia ligands.