Respiratory chain dysfunction plays an important role in human disease and aging. It is now well established that the individual respiratory complexes can be organized into supercomplexes, and structures for these macromolecular assemblies, determined by electron cryo-microscopy, have been described recently. Nevertheless, the reason why supercomplexes exist remains an enigma. The widely held view that they enhance catalysis by channeling substrates is challenged by both structural and biophysical information. Here, we evaluate and discuss data and hypotheses on the structures, roles, and assembly of respiratory-chain supercomplexes and propose a future research agenda to address unanswered questions.