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TeO2 bolometers have been used for many years to search for neutrinoless double beta decay in $130$Te. CUORE, a tonne-scale TeO2 detector array, recently published the most sensitive limit on the half-life, $T1/20ν>1.5×1025$ yr, which corresponds to an upper bound of 140–400 meV on the effective Majorana mass of the neutrino. While it makes CUORE a world-leading experiment looking for neutrinoless double beta decay, it is not the only study that CUORE will contribute to in the field of nuclear and particle physics. As already done over the years with many small-scale experiments, CUORE will investigate both rare decays (such as the two-neutrino double beta decay of $130$Te and the hypothesized electron capture in $123$Te), and rare processes (e.g. dark matter and axion interactions). This paper describes some of the achievements of past experiments that used TeO2 bolometers, and perspectives for CUORE.