Potential detection of non-conserving lepton number processes, such as the neutrinoless double beta decay, constitutes one of the most promising signals of new physics beyond the Standard Model, apart from experiments using high energy collisions. In the neutrinoless double beta decay (0νββ) two neutrons are transformed into two protons and only two electrons are emitted in the final state. This is a very encouraging case due to its implications in fundamental physics since it can only occur if neutrinos are massive and Majorana particles (neutrinos and antineutrinos are identical particles). Additionally, the inverse of the half-life of this process is proportional to the neutrino effective mass. Therefore, an eventual detection of this decay mode would determine the absolute scale of the mass of these elementary particles. However, if the half-life of a given double-beta emitter is experimentally measured, the absolute scale of the neutrino mass can be only determined if the so-called nuclear matrix element (NME), that connects initial and final nuclear states, is accurately known. However, current 0νββ NMEs calculations differ by a factor of three approximately, depending on the nuclear model.
In this contribution I will give an overview of the current status and future perspectives for nuclear matrix elements calculations performed with one of the most promising theoretical methods to compute 0νββ NMEs, namely, the energy density functional method.