Mitochondrial ADP/ATP carriers transport ADP into the mitochondrial matrix for ATP synthesis, and ATP out to fuel the cell, by cycling between cytoplasmic-open and matrix-open states. The structure of the cytoplasmic-open state is known, but it has proved difficult to understand the transport mechanism in the absence of a structure in the matrix-open state. Here, we describe the structure of the matrix-open state locked by bongkrekic acid bound in the ADP/ATP-binding site at the bottom of the central cavity. The cytoplasmic side of the carrier is closed by conserved hydrophobic residues, and a salt bridge network, braced by tyrosines. Glycine and small amino acid residues allow close-packing of helices on the matrix side. Uniquely, the carrier switches between states by rotation of its three domains about a fulcrum provided by the substrate-binding site. Because these features are highly conserved, this mechanism is likely to apply to the whole mitochondrial carrier family. VIDEO ABSTRACT.