Direct Measurements of Neutrino Mass

The turn of the 21st century witnessed a sudden shift in our fundamental understanding of particle physics. While the minimal Standard Model predicts that neutrino masses are exactly zero, the discovery of neutrino oscillations proved the Standard Model wrong. Neutrino oscillation measurements, however, do not shed light on the scale of neutrino masses, nor the mechanism by which those are generated. The neutrino mass scale is most directly accessed by studying the energy spectrum generated by beta decay or electron capture -- a technique dating back to Enrico Fermi's formulation of radioactive decay. In this Article, we review the methods and techniques -- both past and present -- aimed at measuring neutrino masses kinematically. We focus on recent experimental developments that have emerged in the past decade, overview the spectral refinements that are essential in the treatment of the most sensitive experiments, and give a simple yet effective protocol for estimating the sensitivity. Finally, we provide an outlook of what future experiments might be able to achieve.