Bolometers are cryogenic calorimeters which feature excellent energy resolution, low energy threshold, high detection efficiency, flexibility in choice of materials, particle identification capability if operated as hybrid devices. After thirty years of rapid progresses, they represent nowadays a leading technology in several fields: particle and nuclear physics, X-ray astrophysics, cosmology. However, further and substantial developments are required to increase the sensitivity to the levels envisioned by future researches. A review of the challenges to be addressed and potentialities of bolometers in the search for rare nuclear decays is given, with particular emphasis to the neutrinoless double beta decay physics case.