An overview of modern experiments on the search for neutrinoless double decay is presented. The obtained limits on the effective mass of the Majorana neutrino 〈mν〉 are discussed taking into account the uncertainties in the value of the nuclear matrix elements (NMEs) and the value of the axial-vector constant gA. Predictions for the values of 〈mν〉 from the results of oscillation experiments and modern cosmological data are presented. The possibilities of the next generation experiments with sensitivity to 〈mν〉 at the level of ~ 10–50 meV (studying mainly the inverted ordering (IO) region) are discussed. The prospects for studying the normal ordering (NO) region are discussed too. It is shown that the possibilities of studying the NO depend on the mass of the lightest neutrino m0. In the limiting case of small mass (m0 ≤ 0.1 meV), the values of 〈mν〉 ≈ 1–4 meV are predicted, which makes the study of this region inaccessible by the next generation experiments. But there is an allowed region of m0 (7–30 meV) in the framework of NO, where the predicted values for 〈mν〉 could be ~ 10–30 meV and that is quite achievable for the next generation experiments. The possibility to rich in the future sensitivity to 〈mν〉 at the level of ~ 1–10 meV is also discussed.