After an introduction on the various experimental techniques to be adopted in searches for double beta decay, the new approach based on the use of cryogenic low temperature detectors is described. The present results are reported on the limit for neutrinoless double beta decay of 130 Te obtained with the large bolometric detector CUORICINO. This setup consists of 44 cubic crystals of natural TeO 2 with 5 cm sides and 18 crystals of 3 Γ 3 Γ 6 cm 3 . Four of these latter crystals are made with isotopically enriched materials: two in 128 Te and two others in 130 Te. With a sensitive mass of 40.7 kg, this array is by far the most massive running cryogenic detector. The array is operated at a temperature of βΌ10 mK in a dilution refrigerator under a heavy shield in the Gran Sasso Underground Laboratory at a depth of about 3500 m.w.e. The counting rate in the region of neutrinoless double beta decay is 0.18 Β± 0.02 counts keV -1 kg -1 y -1 , among the lowest in this type of experiment. No evidence for neutrinoless double beta decay is found. The corresponding lower limit for the lifetime of this process is 2 Γ 10 24 years at 90% C.L. The resultant upper limit on the effective neutrino mass ranges between 0.2 and 1.0 eV, depending on the theoretically calculated nuclear matrix elements. This constraint is the most restrictive one, except for those obtained with Ge diodes, and is comparable to them. The second part of this report is devoted to the present status of the construction of the larger experiment CUORE (Cryogenic Underground Observatory for Rare Events) formed from 988 bolometers with a cubic TeO 2 absorber of size 5 Γ 5 Γ 5 cm 3 , with a total mass of βΌ750 kg. We present technical details of the CUORE setup as well as of its location and our efforts to reduce radioactive backgrounds.