The phenomenology of the three-neutrino mixing and  the current data on the neutrino masses and mixing parameters will be briefly reviewed. The importance and the physics potential of neutrinoless double beta (bb0nu) decay experiments will be outlined. The ``Standard'' light Majorana neutrino exchange mechanism of the decay, as well as a number of possible ``Non-standard'' mechanisms that can induce the decay, will be considered. The possibility to determine the mechanism(s) generating the bb0nu decay if the decay will be observed, will be analysed in some detail. The current status of the uncertainties in the calculations of the bb0nu decay nuclear matrix elements will be briefly considered.