[en] Experiments to measure the mass of the electron antineutrino from tritium β-decay are reviewed. The spectrum shape and various distributions, needed for the analysis of a measured β-spectrum, are discussed. Their relative importance is pointed out and possible systematic errors are discussed. Recently published measurements gave no indication for a non-zero mass and upper limits in the range 9.3 to 15.4 eV were claimed. These experiments are critically reviewed. It is concluded that the only previous experiment suggesting a mass of about 30 eV, must be wrong. Possible reasons for this are discussed. A brief survey of the masses of the other neutrino types and of neutrino mixing is given and some recent results are summarized. Also the experimental situation of Simpson's 17 keV neutrino is discussed. (author)