The Cryogenic Underground Observatory for Rare Events (CUORE) is the first bolometric experiment searching for neutrino-less double-beta (0[Formula: see text]) decay that has been able to reach the one-ton scale. The detector, located at the Laboratori Nazionali del Gran Sasso in Italy, consists of an array of 988 TeO₂ crystals arranged in a compact cylindrical structure of 19 towers. Following the completion of the detector construction in August 2016, CUORE began its first physics data run in 2017 at a base temperature of about 10 mK. Following multiple optimization campaigns in 2018, CUORE is currently in stable operating mode. In 2019, CUORE released its second result of the search for 0[Formula: see text] corresponding to a TeO₂ exposure of 372.5 kg[Formula: see text]⋅[Formula: see text]yr and a median exclusion sensitivity to a ¹³⁰Te 0[Formula: see text] decay half-life of [Formula: see text] yr. We find no evidence for 0[Formula: see text] decay and set a 90% C.I. Bayesian lower limit of [Formula: see text] yr on the ¹³⁰Te 0[Formula: see text] decay half-life. We present the current status of CUORE’s search for 0[Formula: see text]. We give an update of the CUORE background model and the measurement of the ¹³⁰Te two neutrino double-beta (2[Formula: see text]) decay half-life. Eventually, we show the preliminary results on half-life limits from the analysis of ¹³⁰Te 0[Formula: see text] and 2[Formula: see text] decay to the first 0[Formula: see text] excited state of [Formula: see text]Xe.