The convincing evidences for neutrino flavor oscillation are a clear proof of non-vanishing neutrino masses. However, the absolute values of the neutrino masses cannot be determined by oscillation experiments alone. There are different approaches to set the neutrino mass scale, but the only model-independent one is the investigation of the electron energy spectrum of a \beta decay near its endpoint. The tritium \beta decay experiments at Mainz and Troitsk have recently been finished yielding upper limits of m(\nu _e) < 2.3 {eV}/c² (95\% C.L.). The new Karlsruhe Tritium Neutrino Experiment (KATRIN) aims to improve the sensitivity on the neutrino mass by another order of magnitude down to 0.2 {eV}/c². The status of KATRIN and the ways to handle the extreme challenges are briefly outlined in this paper.

PACS numbers: 14.60.Pq, 3.40.--s, 29.30.Dn