Ultraluminous X-ray sources (ULXs) are off-nuclear X-ray sources with luminosities that exceed the Eddington limit for stellar remnant black holes. This implies either the presence of larger, 'intermediate mass' black holes, or systems that have managed to violate their Eddington limits. Prior to NuSTAR, black hole accretors were widely assumed, even in the latter scenario. However, in 2014 NuSTAR made the remarkable discovery that one of these systems, M82 X-2, is in fact powered by an accreting, pulsating neutron star (i.e., a pulsar), firmly demonstrating that this is a source radiating at ~100 times Eddington. Much about these systems remains shrouded in mystery: it is not clear how significantly neutron star accretors contribute to the demographics of the overall ULX population, and it is also not understood how these sources are able to radiate at such extreme levels. As of today, roughly half a dozen neutron star ULXs are known, including systems radiating up to 500 times the Eddington limit. I will discuss the current state of this rapidly evolving field.