Present limits on neutrino masses are briefly reviewed, along with cosmological and astrophysical hints from dark matter, solar and atmospheric neutrino observations that suggest neutrino masses. These would imply many possible new phenomena such as neutrinoless $����$ decay, lepton flavour violating processes such as neutrino oscillations, $��\ra e ��$, $��\ra 3 e $, $��\ra e$ conversion in nuclei, as well as two-body decays with the emission of a superweakly interacting spin zero particle, called majoron, e.g. $��\ra e + J$. All of these processes may occur at levels consistent with present or planned experimental sensitivities. The underlying physics may also be probed at the high energies accessible at LEP, through related Z decay processes. Another possible, albeit quite indirect, manifestation of massive neutrinos is in Higgs physics. As an example I discuss the possibility of an invisibly decaying Higgs, a quite generic feature of majoron models where the lepton number is spontaneously violated close to the electroweak scale.

12 pages, latex, 8 figs. available by fax, FTUV/93-52, Invited Talk at Third Workshop on Theory and Phenomenology of Underground Physics, TAUP93, Gran Sasso, Sept. 1993, Italy. Expanded version of earlier talk at the Int. School of Nuclear Physics, Erice, Italy, Sept. 1993