Are neutrinos Dirac or Majorana particles?

In spite of the general belief that neutrinos are Majorana particles, their character should be revealed experimentally. We begin by discussing why it is so difficult in terrestrial experiments. If neutrinos are Majorana particles, the first signal should come from neutrinoless double beta decay. Still the search for such a decay of various nuclei is negative. We outline how the present knowledge of neutrino masses and mixing matrix elements combined with the bound from (beta beta)(0v) decay could help to determine their nature.