  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 $(\beta \beta)_{0\nu}$ decay could help to determine their
nature.
