The impact in neutrino physics of the recent results on oscillations and the consequent need to measure the value of the neutrino mass are briefly discussed. Different detectors are developed and many experiments are planned to determine this mass, or at least to put an upper limit on it. This can be done by exploring the upper region of the spectrum of low energy β decays or by searching for neutrinoless double-beta decay (DBD). A possible evidence for neutrinoless DBD has been presented by a subset of the Heidelberg-Moscow Collaboration, but experiments of similar sensitivity like CUORICINO and NEMO do not confirm these results. They are however unable to confute it, due to the uncertainties on the calculation of the nuclear matrix elements in the evaluation of the absolute value of the neutrino mass. Various second-generation DBD experiments, of which one (CUORE) is presently in construction, aim to reach the sensitivity on the absolute Majorana neutrino mass predicted by the oscillation experiments under the inverse hierarchy hypothesis.