CUORE is an experiment intended to investigate rare events like the double beta decay and the interaction of cold dark matter and solar axions. It consists of a tightly packed array of 1000 TeO 2 bolometers, having a mass of 750 g each, operating in the Laboratori Nazionali del Gran Sasso (LNGS) in Italy. A first step towards CUORE is CUORICINO, an experiment with 40.7 kg of TeO 2 running since the beginning of 2003 in Gran Sasso. In this paper, the CUORE project is described, the first results of CUORICINO for the neutrinoless double beta decay of 130 Te are given, and the physics potential and prospects of both CUORICINO and CUORE are presented.