Interferometry among telescope arrays has become a standard technique in astronomy, allowing greater resolving power than would be available to any plausibly-sized single telescope. For radio frequencies, interferometry can be performed robustly even between telescopes spread across the planet. Interferometry between telescopes operating at infrared or optical frequencies is also possible, but fewer photons arrive at these high frequencies, making interferometry much more difficult. In today's IR and optical interferometric arrays, photons arriving at different telescopes must be physically brought together for the interference measurement, limiting baselines to a few hundred meters at most because of phase fluctuations and photon loss in the transmission. I will discuss how to apply quantum repeaters to the task of optical and infrared interferometry to allow telescope arrays with much longer baselines than existing facilities.