We summarize the radio synchrotron background workshop that took place July 19-21, 2017 at the University of Richmond. This first scientific meeting dedicated to the topic was convened because current measurements of the diffuse radio monopole reveal a surface brightness that is several times higher than can be straightforwardly explained by known Galactic and extragalactic sources and processes, rendering it by far the least well understood photon background at present. It was the conclusion of a majority of the participants that the radio monopole level is at or near that reported by the ARCADE 2 experiment and inferred from several absolutely calibrated zero level lower frequency radio measurements, and unanimously agreed that the production of this level of surface brightness, if confirmed, represents a major outstanding question in astrophysics. The workshop reached a consensus on the next priorities for investigations of the radio synchrotron background.