The presently most wanted information on neutrino properties concerns their mass values and their transformation properties under charge conjugation. The recent oscillation experiments prove that at least one of the three neutrino species has a non-vanishing rest mass and that the lepton flavour is not conserved. These findings have to be supplemented by data from phenomena of different kind in order to deduce the information needed. The most promising method proposed thus far to determine Majorana neutrino mass and thus to answer the two leading questions is to observe the neutrino-less double beta decay and to measure its rate. The physics of this process is discussed and the on-going and planned experimental search is reviewed. This search concentrates on the 0{⁺} \rightarrow 0{⁺} ground-to-ground state decay of {\beta ^-} {\beta ^-} emitters using calorimetric or {\beta ^-} - {\beta ^-} coincidence tracking techniques. The {\beta ⁺} {\beta ⁺} or {\beta ⁺}EC decays are usually considered as less favourable because of longer half-lives, even though they offer some advantages in combating the background. The recent proposition of measuring the monoenergetic photon spectra accompanying the radiative neutrino-less double electron capture decay is discussed. The experimental advantages of this technique may off-set the generally longer life-times expected.

PACS numbers: 23.40.--s, 23.40.Bw, 14.60.Pq