Biological energy conversion in mitochondria is carried out by the membrane protein complexes of the respiratory chain and the mitochondrial ATP synthase in the inner membrane cristae. Recent advances in electron cryomicroscopy have made possible new insights into the structural and functional arrangement of these complexes in the membrane, and how they change with age. This review places these advances in the context of what is already known, and discusses the fundamental questions that remain open but can now be approached.