  With a mass at least six orders of magnitudes smaller than the mass of an
electron -- but non-zero -- neutrinos are a clear misfit in the Standard Model
of Particle Physics. On the one hand, its tiny mass makes the neutrino one of
the most interesting particles, one that might hold the key to physics beyond
the Standard Model. On the other hand this minute mass leads to great
challenges in its experimental determination. Three approaches are currently
pursued: An indirect neutrino mass determination via cosmological observables,
the search for neutrinoless double $\beta$-decay, and a direct measurement
based on the kinematics of single $\beta$-decay. In this paper the latter will
be discussed in detail and the status and scientific reach of the current and
near-future experiments will be presented.

Nuclear Experiment;Instrumentation and Detectors