Different from some more specialised short reviews, here a general although not encyclopaedic survey of the function, metabolic role, structure and mechanism of the ADP/ATP transport in mitochondria is presented. The obvious need for an "old fashioned" review comes from the gateway role in metabolism of the ATP transfer to the cytosol from mitochondria. Amidst the labours, 40 or more years ago, of unravelling the role of mitochondrial compartments and of the two membranes, the sequence of steps of how ATP arrives in the cytosol became a major issue. When the dust settled, a picture emerged where ATP is exported across the inner membrane in a 1:1 exchange against ADP and where the selection of ATP versus ADP is controlled by the high membrane potential at the inner membrane, thus uplifting the free energy of ATP in the cytosol over the mitochondrial matrix. Thus the disparate energy and redox states of the two major compartments are bridged by two membrane potential responsive carriers to enable their symbiosis in the eukaryotic cell. The advance to the molecular level by studying the binding of nucleotides and inhibitors was facilitated by the high level of carrier (AAC) binding sites in the mitochondrial membrane. A striking flexibility of nucleotide binding uncovered the reorientation of carrier sites between outer and inner face, assisted by the side specific high affinity inhibitors. The evidence of a single carrier site versus separate sites for substrate and inhibitors was expounded. In an ideal setting principles of transport catalysis were elucidated. The isolation of intact AAC as a first for any transporter enabled the reconstitution of transport for unravelling, independently of mitochondrial complications, the factors controlling the ADP/ATP exchange. Electrical currents measured with the reconstituted AAC demonstrated electrogenic translocation and charge shift of reorienting carrier sites. Aberrant or vital para-functions of AAC in basal uncoupling and in the mitochondrial pore transition were demonstrated in mitochondria and by patch clamp with reconstituted AAC. The first amino acid sequence of AAC and of any eukaryotic carrier furnished a 6-transmembrane helix folding model, and was the basis for mapping the structure by access studies with various probes, and for demonstrating the strong conformation changes demanded by the reorientation mechanism. Mutations served to elucidate the function of residues, including the particular sensitivity of ATP versus ADP transport to deletion of critical positive charge in AAC. After resisting for decades, at last the atomic crystal structure of the stabilised CAT-AAC complex emerged supporting the predicted principle fold of the AAC but showing unexpected features relevant to mechanism. Being a snapshot of an extreme abortive "c-state" the actual mechanism still remains a conjecture.