This review focuses on key components of respiratory and photosynthetic energy-transduction systems: the cytochrome bc1 and b6f (Cytbc1/b6f) membranous multisubunit homodimeric complexes. These remarkable molecular machines catalyze electron transfer from membranous quinones to water-soluble electron carriers (such as cytochromes c or plastocyanin), coupling electron flow to proton translocation across the energy-transducing membrane and contributing to the generation of a transmembrane electrochemical potential gradient, which powers cellular metabolism in the majority of living organisms. Cytsbc1/b6f share many similarities but also have significant differences. While decades of research have provided extensive knowledge on these enzymes, several important aspects of their molecular mechanisms remain to be elucidated. We summarize a broad range of structural, mechanistic, and physiological aspects required for function of Cytbc1/b6f, combining textbook fundamentals with new intriguing concepts that have emerged from more recent studies. The discussion covers but is not limited to (i) mechanisms of energy-conserving bifurcation of electron pathway and energy-wasting superoxide generation at the quinol oxidation site, (ii) the mechanism by which semiquinone is stabilized at the quinone reduction site, (iii) interactions with substrates and specific inhibitors, (iv) intermonomer electron transfer and the role of a dimeric complex, and (v) higher levels of organization and regulation that involve Cytsbc1/b6f. In addressing these topics, we point out existing uncertainties and controversies, which, as suggested, will drive further research in this field.