Neutrino-less double beta decays (0), which violate the lepton number conservation law by ÁL ¼ 2, are of great interest for studying the fundamental properties of neutrinos beyond the standard electroweak theory. High-sensitivity 0 studies with mass sensitivities of the solar and atmosphericmasses are crucial for studying the Majorana nature of 's, the mass spectrum, the absolute -mass scale, the Majorana CP phases and other fundamental properties of neutrinos and weak interactions. Actually, high-sensitivity experiments of 0 are the unique and practical method for studying all these fundamental properties of neutrinos in the foreseeable future. On the basis of the recent oscillation studies, the effective mass sensitivity required for observing the 0 rate is of the order of the atmospheric mass scale of m A $ 50 meV in the case of the inverted mass hierarchy and of the order of the solar mass scale of m S $ 8 meV in the case of the normal hierarchy. The present detectors with sensitivities of 150 -300 meV are effective in the case of the quasi-degenerate mass spectrum. Future detectors with higher sensitivities of the orders of m A -m S , using different nuclei and methods (calorimetric, spectroscopic), are indispensable for establishing 0. Theoretical and experimental studies for evaluating nuclear matrix elements M 0 within 20 -30% are important for extracting the sensible mass from the 0 rate. Charge exchange reactions by means of nuclear, electron and probes provide useful data for M 0 . International collaboration for experimental and theoretical works are encouraged to perform next-generation experiments. High-sensitivity detectors can be used for studying rare nuclear processes such as solar 's, dark matter, charge nonconservation, and nucleon decays. This report is a brief review of double beta decays and neutrinos with emphasis on highsensitivity 0 studies for the Majorana mass.