The recent general acceptance of the proton-pumping function of cytochrome oxidase has stimulated discussion and experiment on possible underlying molecular mechanisms. Adequate experimental design requires clear understanding of the theoretical principles governing such a linked function. The increasing structural knowledge of cytochrome oxidase also contributes to a present-day requirement of more precise chemical and physical description of redox-linked proton translocation, which is the fundamental process underlying conservation of energy from aerobic metabolism in all eukaryotes and many bacteria. This essay is based on our original theoretical treatment of this problem, which is expanded here to include discussion of more recent analyses by others, classification of different types of coupling principles, as well as some concrete proposed molecular mechanisms. The latter will be analysed qualitatively, and in some cases quantitatively where this is possible, using a common theoretical framework to help comparison between models. Experimental findings relevant to this problem will be critically reviewed, and some suggestions will be made to stimulate further experiments dedicated to clarify the problem.