Black holes are the simplest macroscopic objects, and provide unique tests of general relativity. They have been compared to the hydrogen atom in quantum mechanics. Here, we establish a few facts about the simplest systems bound by gravity: black hole binaries. We provide strong evidence for the existence of "global" photosurfaces surrounding the binary, and of binary quasinormal modes leading to the exponential decay of massless fields when the binary spacetime is slightly perturbed. These two properties go hand in hand, as they do for isolated black holes. The binary quasinormal modes have a high quality factor and may be prone to resonant excitations. Finally, we show that energy extraction from binaries is generic and we find evidence of a new mechanism-akin to the Fermi acceleration process-whereby the binary transfers energy to its surroundings in a cascading process. The mechanism is conjectured to work when the individual components spin, or are made of compact stars.