A brief overview is given of the studies of high-temperature interface superconductivity based  on  atomic-layer-by-layer  molecular  beam  epitaxy  (ALL-MBE).  A  number  of difficult materials science and physics questions have been tackled, frequently at the expense  of  some  technical  tour  de  force,  and  sometimes  even  by  introducing  new techniques. ALL-MBE is especially suitable to address questions related to surface and interface physics. Using this technique, it has been demonstrated that high-temperature superconductivity can occur in a single copper oxide layer—the thinnest superconductor known.  It  has  been  shown  that  interface  superconductivity  in  cuprates  is  a  genuine electronic effect—it arises from charge transfer (electron depletion and accumulation) across the interface driven by the difference in chemical potentials rather than from cation diffusion and mixing. We have also understood the nature of the superconductor–insulator phase transition as a function of doping. However, a few important questions, such as the mechanism of interfacial enhancement of the critical temperature, are still outstanding.

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doi:10.1098/rsta.2012.0219