  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, $T_{1/2}^{0\nu} > 1.5
\times 10^{25}\,$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.
