Double Beta Decay provides a very sensitive test of lepton‐number conservation. Howver, decay rates are so small that it has not yet been possible to unequivocally detect a Double Beta Decay event directly; so much the more important is the data obtained by the ‘‘geochemical’’ method where one detects the Double Beta Decay products which have accumulated in natural minerals during long geological time periods. In that order, I discuss ‐the principles of the geochemical method, its strength and its limitations ‐the available data ‐new results on the 128Te−130Te system theoretical implications of the data concerning the electron neutrino restmass and lepton‐number conservation. A limit of m ν≤5.6 eV (95% confidence) has been obtained from our recent 128Te−130Te‐measurements.