Neutrinoless double beta decay and nuclear matrix elements

The fundamental importance of searching for neutrinoless double-beta decay (0-decay) is widely recognized. Observation of the decay would tell us that the total lepton number is not conserved and that, consequently, neutrinos are massive Majorana fermions. The 0-decay is discussed in context of neutrino oscillation data. The perspectives of the experimental 0-decay searches are analyzed. The importance of reliable determination of the 0-decay nuclear matrix elements is pointed out