Cosmological neutrino bounds for non-cosmologists

I briefly review cosmological bounds on neutrino masses and the underlying gravitational physics at a level appropriate for readers outside the field of cosmology. For the case of three massive neutrinos with standard model freezeout, the current 95% upper limit on the sum of their masses is 0.42eV. I summarize the basic physical mechanism making matter clustering such a sensitive probe of massive neutrinos. I discuss the prospects of doing still better in coming years using tools such as lensing tomography, approaching a sensitivity around 0.03eV. Since the lower bound from atmospheric neutrino oscillations is around 0.05eV, upcoming cosmological measurements should detect neutrino mass if the technical and fiscal challenges can be met.