Recent years have witnessed many exciting breakthroughs in neutrino physics. The detection of neutrino oscillations has proved that neutrinos are massive particles but the assessment of their absolute mass scale is still an outstanding challenge in today particle physics and cosmology. Due to their abundance as big-bang relics, massive neutrinos strongly affect the large-scale structure and dynamics of the universe. In addition, the knowledge of the scale of neutrino masses, together with their hierarchy pattern, is invaluable to clarify the origin of fermion masses beyond the Higgs mechanism. The mass hierarchy is not the only missing piece in the puzzle. Theories of neutrino mass generation call into play Majorana neutrinos and there are experimental observations pointing to the existence of sterile neutrinos in addition to the three ones weakly interacting. Since low temperature detectors were first proposed for neutrino physics experiments in 1984, there have been impressive technical progresses: today this technique offers the high energy resolution and scalability required for leading edges and competitive experiments addressing the still open questions.