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, shed light neither on the scale of neutrino masses, nor on 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.

21世纪的转折见证了我们对粒子物理学的基本理解的突然转变。尽管最小标准模型预测中微子质量恰好为零，但是中微子振荡的发现证明标准模型是错误的。然而，中微子的振荡测量既没有揭示中微子质量的规模，也没有揭示产生中微子质量的机理。通过研究β衰变或电子俘获所产生的能谱，可以最直接地访问中微子质量尺度。这项技术可以追溯到恩里科·费米（Enrico Fermi）提出的放射性衰变公式。在本文中，我们将回顾过去和现在的方法和技术，这些方法和技术旨在以运动学方式测量中微子质量。我们专注于过去十年中出现的最新实验性发展，概述了在最灵敏的实验中必不可少的光谱优化方法，并给出了一个简单而有效的方法来估算灵敏性。最后，我们展望了未来的实验可能实现的目标。