AbstractThe Cryogenic Underground Observatory for Rare Events (CUORE) is the first cryogenic experiment searching for $0ν β β $ 0 ν β β decay that has been able to reach the one-tonne mass scale. The detector, located at the Laboratori Nazionali del Gran Sasso (LNGS) in Italy, consists of an array of 988 ${\mathrm{TeO}}_{2}$ TeO 2 crystals arranged in a compact cylindrical structure of 19 towers. CUORE began its first physics data run in 2017 at a base temperature of about 10 mK and in April 2021 released its $3{\mathrm{rd}}$ 3 rd result of the search for $0ν β β $ 0 ν β β , corresponding to a tonne-year of $\mathrm{TeO}_{2}$ TeO 2 exposure. This is the largest amount of data ever acquired with a solid state detector and the most sensitive measurement of $0ν β β $ 0 ν β β decay in ${}^{130}\mathrm{Te}$ 130 Te ever conducted . We present the current status of CUORE search for $0ν β β $ 0 ν β β with the updated statistics of one tonne-yr. We finally give an update of the CUORE background model and the measurement of the ${}^{130}\mathrm{Te}$ 130 Te $2ν β β $ 2 ν β β decay half-life and decay to excited states of ${}^{130}\mathrm{Xe}$ 130 Xe , studies performed using an exposure of 300.7 kg yr.