  The sum of the masses of the three neutrino mass eigenstates is now
constrained both from above and below, and lies between 55 and 6900 meV. The
lower limit is set by neutrino oscillations and the fact that masses are
non-negative. The upper limit is set by laboratory measurements on the beta
decay of tritium. These determinations share a common characteristic of being
essentially model independent, or "direct." The clustering on large scales in
the universe depends on this quantity, and, within the framework of Lambda-CDM
cosmology, favors a mass sum below about 600 meV. In this article, the
laboratory approach to neutrino mass via beta decay is emphasized, particularly
an experiment now under construction, KATRIN, on the beta decay of tritium.
Another candidate beta-active nuclide, Re-187, offers an advantage in phase
space but calls for a very different experimental approach.
