The nature of the Fe-O-2 bonding in oxy-myoglobin was probed by theoretical calculations: (a) QM/MM (hybrid quantum mechanical/molecular mechanical) calculations using DFT/MM and CASSCF/MM methods and (b) gas-phase calculations using DFT (density functional theory) and CASSCF (complete active space self-consistent field) methods. Within the protein, the O-2 is hydrogen bonded by His64 and the complex feels the bulk polarity of the protein. Removal of the protein causes major changes in the complex. Thus, while CASSCF/MM and DFT/MM are similar in terms of state constitution, degree Of O-2 charge, and nature of the lowest triplet state, the gas-phase CASSCF(g) species is very different. Valence bond (VB) analysis of the CASSCF/MM wave function unequivocally supports the Weiss bonding mechanism. This bonding arises by electron transfer from heme-Fe-II to O-2 and the so formed species coupled then to a singlet state Fe-III-O-2(-) that possesses a dative pi(Fe-O) bond and a weakly coupled pi(Fe-O-2) bond pair. The bonding mechanism in the gas phase is similar, but now the sigma(Fe-O) bond involves higher back-donation from O-2(-) to Fe-III, while the constituents of pi(Fe-O-2) bond pair have greater delocalization tails. The protein thus strengthens the Fe-III-O-2(-) character of the complex and thereby affects its bonding features and the oxygen binding affinity of Mb. The VB model is generalized, showing how the protein or the axial ligand of the oxyheme complex can determine the nature of its bonding in terms of the blend of the three bonding models: Weiss, Pauling, and McClure-Goddard.