The discovery of neutrino oscillations gives us proof that neutrinos have mass, the first direct contradiction of the minimal standard model of particle physics. But how much mass? The mass is needed to build the new standard model, and to help pin down the equation of state of dark energy and the evolution of structure in cosmology. Oscillations cannot give a number for the mass, other than to tell us that the average of the three masses must be at least 0.02 eV. Laboratory measurements of the beta spectrum of tritium have steadily advanced: the masses are now known to be less than 2 eV. A very large and ambitious experiment called KATRIN that offers an order of magnitude gain in sensitivity is taking shape in Germany. And a novel, very different idea called “Project 8” has just passed its proof-of-concept test, a scheme that might have even greater sensitivity.