  The investigation of the endpoint region of the tritium beta decay spectrum
is still the most sensitive direct method to determine the neutrino mass scale.
In the nineties and the beginning of this century the tritium beta decay
experiments at Mainz and Troitsk have reached a sensitivity on the neutrino
mass of 2 eV/c^2 . They were using a new type of high-resolution spectrometer
with large sensitivity, the MAC-E-Filter, and were studying the systematics in
detail. Currently, the KATRIN experiment is being set up at Forschungszentrum
Karlsruhe, Germany. KATRIN will improve the neutrino mass sensitivity by one
order of magnitude down to 0.2 eV/c^2, sufficient to cover the degenerate
neutrino mass scenarios and the cosmologically relevant neutrino mass range.
