Haem-copper oxygen reductases are transmembrane protein complexes that reduce dioxygen to water and pump protons across the mitochondrial or periplasmatic membrane, contributing to the transmembrane difference of electrochemical potential. Seven years ago we proposed a classification of these enzymes into three different families (A, B and C), based on the amino acid residues of their proton channels and amino acid sequence comparison, later supported by the so far identified characteristics of the catalytic centre of members from each family. The three families have in common the same general structural fold of the catalytic subunit, which contains the same or analogous prosthetic groups, and proton channels. These observations raise the hypothesis that the mechanisms for dioxygen reduction, proton pumping and the coupling of the two processes may be the same for all these enzymes. Under this hypothesis, they should be performed and controlled by the same or equivalent elements/events, and the identification of retained elements in all families will reveal their importance and may prompt the definition of the enzyme operating mode. Thus, we believe that the search for a minimum common denominator has a crucial importance, and in this article we highlight what is already established for the haem-copper oxygen reductases and emphasize the main questions still unanswered in a comprehensive basis.