Neutrinoless double beta decay (0vββ) is one of the most sensitive probes for physics beyond the Standard Model, providing unique information on the nature and masses of neutrinos. In order to explore the so-called inverted neutrino mass hierarchy region a further improvement on the upcoming 0vββ experiment is needed. In this respect, scintillating bolometers are the suitable technology for achieving such goal: they ensure excellent energy resolution and highly efficient particle discrimination. The LUCIFER project aims at deploying the first array of enriched scintillating bolometers for the investigation of 0vββ of 82Se. The matrix which embeds the source is an array of Zn 82Se crystals, where enriched 82Se is used as decay isotope. Taking advantage of the large Q-value (2997 keV) and of the particle discrimination, the expected background rate in the region of interest is as low as 10-3 c/keV/kg/y. The foreseen sensitivity after 2 years of live time will be 1.8×1025 years. We will report on the potential of such technology and on the present status of the project.