Warburg showed in 1929 that the photochemical action spectrum for CO dissociation from cytochrome c oxidase is that of a heme protein. Keilin had shown that cytochrome a does not react with oxygen, so he did not accept Warburg''s view until 1939, when he discovered cytochrome a ₃. The dinuclear cytochrome a ₃-Cu_B unit was found by EPR in 1967, whereas the dinuclear nature of the Cu_A site was not universally accepted until oxidase crystal structures were published in 1995. There are negative redox interactions between cytochrome a and the other redox sites in the oxidase, so that the reduction potential of a particular site depends on the redox states of the other sites. Calculated electron-tunneling pathways for internal electron transfer in the oxidase indicate that the coupling-limited rates are 9×10⁵ (Cu _A a) and 7×10⁶ s^–1 (a a ₃); these calculations are in reasonable agreement with experimental rates, after corrections are made for driving force and reorganization energy. The best Cu_A-a pathway starts from the ligand His204 and not from the bridging sulfur of Cys196, and an efficient a-a ₃ path involves the heme ligands His378 and His376 as well as the intervening Phe377 residue. All direct paths from Cu_A to a ₃ are poor, indicating that direct Cu_A a ₃ electron transfer is much slower than the Cu_A a reaction. The pathways model suggests a means for gating the electron flow in redox-linked proton pumps.