The paper reviews recent experiments on tritium beta spectroscopy searching for the absolute value of the electron neutrino mass $m( u_e)$. By use of dedicated electrostatic filters with high acceptance and resolution, the uncertainty on the observable $m^2( u_e)$ has been pushed down to about 3 eV$^2$. The new upper limit of the mass is $m( u_e) < 2$ eV at 95% C.L. In view of erroneous and unphysical mass results obtained by some earlier experiments in beta decay, particular attention is paid to systematic effects. The mass limit is discussed in the context of current neutrino research in particle- and astrophysics. A preview is given of the next generation of beta spectroscopy experiments currently under development and construction; they aim at lowering the $m^2( u_e)$-uncertainty by another factor of 100, reaching a sensitivity limit $m( u_e) < 0.2$ eV.
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