Cytochrome c oxidase (COX), the terminal enzyme of mitochondrial electron transport chain, couples electron transport to oxygen with generation of proton gradient indispensable for the production of vast majority of ATP molecules in mammalian cells. The review summarizes current knowledge of COX structure and function of nuclear-encoded COX subunits, which may modulate enzyme activity according to various conditions. Moreover, some nuclear-encoded subunits posess tissue-specific and development-specific isoforms, possibly enabling fine-tuning of COX function in individual tissues. The importance of nuclear-encoded subunits is emphasized by recently discovered pathogenic mutations in patients with severe mitopathies. In addition, proteins substoichiometrically associated with COX were found to contribute to COX activity regulation and stabilization of the respiratory supercomplexes. Based on the summarized data, a model of three levels of quaternary COX structure is postulated. Individual structural levels correspond to subunits of the i) catalytic center, ii) nuclear-encoded stoichiometric subunits and iii) associated proteins, which may constitute several forms of COX with varying composition and differentially regulated function.