The majority of adenosine triphosphate (ATP) powering cellular processes in eukaryotes is produced by the mitochondrial F1Fo ATP synthase. Here, we present the atomic models of the membrane Fo domain and the entire mammalian (ovine) F1Fo, determined by cryo-electron microscopy. Subunits in the membrane domain are arranged in the 'proton translocation cluster' attached to the c-ring and a more distant 'hook apparatus' holding subunit e. Unexpectedly, this subunit is anchored to a lipid 'plug' capping the c-ring. We present a detailed proton translocation pathway in mammalian Fo and key inter-monomer contacts in F1Fo multimers. Cryo-EM maps of F1Fo exposed to calcium reveal a retracted subunit e and a disassembled c-ring, suggesting permeability transition pore opening. We propose a model for the permeability transition pore opening, whereby subunit e pulls the lipid plug out of the c-ring. Our structure will allow the design of drugs for many emerging applications in medicine.