Heme-copper oxidases (HCOs) are terminal enzymes on the mitochondrial or bacterial respiratory electron transport chain, which utilize a unique heterobinuclear active site to catalyze the 4H+/4e- reduction of dioxygen to water. This process involves a proton-coupled electron transfer (PCET) from a tyrosine (phenolic) residue and additional redox events coupled to transmembrane proton pumping and ATP synthesis. Given that HCOs are large, complex, membrane-bound enzymes, bioinspired synthetic model chemistry is a promising approach to better understand heme-Cu-mediated dioxygen reduction, including the details of proton and electron movements. This review encompasses important aspects of heme-O2 and copper-O2 (bio)chemistries as they relate to the design and interpretation of small molecule model systems and provides perspectives from fundamental coordination chemistry, which can be applied to the understanding of HCO activity. We focus on recent advancements from studies of heme-Cu models, evaluating experimental and computational results, which highlight important fundamental structure-function relationships. Finally, we provide an outlook for future potential contributions from synthetic inorganic chemistry and discuss their implications with relevance to biological O2-reduction.