We explore the complementarity between terrestrial neutrino oscillation experiments and astrophysical/cosmological measurements in probing the existence of sterile neutrinos. We find that upcoming accelerator neutrino experiments will not improve on constraints by the time they are operational, but that reactor experiments can already probe parameter space beyond the reach of Planck. We emphasize the tension between cosmological experiments and reactor antineutrino experiments and enumerate several possibilities for resolving this tension. † It is, by hypothesis, not possible to directly detect sterile neu-arXiv:1905.03254v1 [hep-ph]