Status of the search for neutrinoless double beta decay, circa 2015

Following [Phys. Rev. D 90, 033005 (2014)], we review the present status and the future perspectives on the search for neutrinoless double beta decay (0vββ) within the hypothesis that its rate is dominated by the Majorana mass of ordinary neutrinos. We show updated predictions on 0vββ coming from neutrino oscillations, we assess the sensitivity of present and future experiments and we focus on the effects of the uncertainties coming from nuclear physics. In particular, the impact of the quenching of the axial vector coupling constant in the nuclear medium is analyzed. Finally, we stress the important interplay between 0vββ and cosmology. In fact, taking into account the most recent indications on neutrino masses coming from cosmology, we discuss whether it could be possible to measure the Majorana phases and/or discriminate the two neutrino mass hierarchies.