Contributed Review: The saga of neutrinoless double beta decay search with TeO2 thermal detectors.

Neutrinoless double beta decay (0νββ) is a direct probe of physics beyond the standard model. Its discovery would demonstrate that the lepton number is not a symmetry of nature and would provide us with unique information on the nature and mass of the neutrinos. Among the experimental techniques employed in the investigation of this rare process, thermal detectors fulfill the requirements for a powerful search, showing an excellent energy resolution and the possibility of scaling to very large masses. In this work, we review the long chain of bolometric experiments based on TeO2 crystals that were and continue to be carried out at the Laboratori Nazionali del Gran Sasso (Italy), searching for 0νββ of 130Te. We illustrate the progress and improvements achieved in almost thirty years of measurements and compare the various performance and results. We describe the several steps that led to the CUORE detector, the latest of this series and presently in data taking, and we highlight the challenges that a next bolometric experiment will face in order to further improve the sensitivity, especially concerning the background abatement. Finally, we emphasize the advantages of 130Te in the search for 0νββ with a further future experiment.