The search for Majorana neutrinos with Neutrinoless Double Beta Decays: from Cuoricino to Lucifer experiment

The study of neutrino properties is one of the fundamental challenges in particle physics nowadays. Fifty years of investigations established that neutrinos are massive but the absolute mass scale has not yet been measured. Moreover its true nature is still unknown. Is the neutrino its own antiparticle (thus violating the lepton number) as proposed by Majorana in 1937? The only way to probe the neutrino nature is through the observation of Neutrinoless Double Beta Decay (0 nu beta beta), a very rare spontaneous nuclear transition which emits two electrons and no neutrinos. In this paper, after a brief introduction to the theoretical framework of Majorana's neutrino, a presentation of experimental challenges posed by 0 nu beta beta search will be given as well as an overview of present status and future perpectives of experiments.