Neutrinoless Double Beta Decay (0v-DBD) is in a central position for the study of elementary particles and fundamental interactions. It has strong implications on topics of cosmological character as well. After the discovery of neutrino flavor oscillations, crucial issues remain open, such as the absolute neutrino mass scale and the mass hierarchy, together with the quest of the neutrino nature: Dirac or Majorana fermion? The purpose of this project, named LUMINEU, is to set the bases for the realization of a next-generation 0v-DBD experiment with unprecedented sensitivity. To succeed, LUMINEU proposes to reduce the residual background due to alpha particles owing to the simultaneous measurement of the light and the heat generated in a nuclear event. This double read-out approach will allow rejecting interactions due to alpha particles with efficiency close to 1. If the scintillating bolometers contain a candidate to 0v-DBD with transition energy higher than the natural gamma radioactivity end-point (2.6 MeV), the rejection of alpha particles enables a virtually zero-background experiment for the exposures required to scrutinize the inverted hierarchy region of the neutrino mass pattern. LUMINEU envisages the study of large ZnMoO4 scintillating crystals, containing the excellent candidate 100Mo, which is featured by a Q-value around 3 MeV. The ZnMoO4 crystals will be grown with an advanced technique which warrants excellent crystal quality, extreme purity and negligible waste of the starting material. A mass of 400 g for the single module is foreseen. The rejection of alpha particles is correlated to the quality of the light measurement. A special effort will be dedicated to the optimization of the scintillation light detectors in terms of energy threshold, size, reproducibility and time response. Reducing this time would be the key in case of ultimate background due to the pile-up of standard DBD with neutrino, particularly relevant in the case of 100Mo. As a consequence, beside the production of standard semiconductor sensors (NTD) by nuclear transmutation, new sensors will be studied: high impedance superconductive films and metallic paramagnetic thermometers. The coupling of such sensors to massif crystals without loss in their nominal performances would be a strong innovation. This result would have an impact on astroparticle physics beyond the 0v-DBD. This may lead to important advancements in dark matter direct detection in EDELWEISS-3 and EURECA. The progress in thermal sensors and their coupling, will lead to the improvement of the energy resolution and threshold of the heat channel and to a better sensitivity to WIMPs in particular at low masses. LUMINEU will take advantage of contributions from both communities. In the same time, both field of research will take benefit of LUMINEU’s developments. The results on the scintillating crystals and on the light detectors will enable a 0v-DBD pilot experiment performed in an underground environment and containing a considerable amount of enriched molybdenum (about 1 kg). After the conclusion of LUMINEU, the realization of a large-scale experiment looking at the 20 meV region for the effective neutrino mass will be just a matter of political will and fund availability.