Neutrinos: Dirac or Majorana?

The problem of the nature of the neutrino, namely i f it is a massless Dirac particle different from its antineutrino or a Majorana particle with finite mass, is discussed. The question is related to the recent results showing the presence of neutrino oscillations clearly indicating that the difference between the squared mass of neutrinos of different flavours is different from zero. Neutrinoless double beta decay (DBD) is at present the most powerful tool to determine the effective value of the mass of a Majorana neutrino. The results already obtained in this lepton violating process will be reported and the two pres ently running DBD experiments briefly discussed. The future second generation experiments will be reviewed with special emphasis to those already partially approved. In conclusion the peculiar and interdisciplinary nature of these searches will be stressed in their exciting aim to discover if neutrino is indeed a Majorana particle