The nature of dark matter (DM) is unknown, with a vast array of possibilities able to account for the missing mass of the universe. A predictive subset of DM models has DM in thermal equilibrium with Standard Model particles in the early universe. A well-known example of this is the Weakly-Interacting Massive Particle (WIMP) with an electroweak-scale mass. However, as direct searches for WIMP-nucleus interactions set stronger and stronger limits, attention has turned to less well-explored DM candidates. Sub-MeV thermal relics, in particular, have received little attention, in part due to the apparently stringent bounds from astrophysics and cosmology. For example, such particles contribute to the energy density of the universe at the time of nucleosynthesis and recombination. The resulting constraints on extra degrees of freedom typically exclude even the simplest of such dark sectors. I will describe the physics that leads to these bounds and show that if a sub-MeV dark sector entered equilibrium with the Standard Model after neutrino-photon decoupling, these constraints are alleviated. This scenario naturally arises in theories of neutrino mass generation through the spontaneous breaking of lepton number. Dark matter relic abundance in these models independently motivates the MeV scale. This scenario will be decisively tested by future measurements of the cosmic microwave background and large scale structure of the universe.