CUPID-0 is the first pilot experiment of CUPID, a next-generation project to search for neutrinoless double beta decay (0νDBD) with scintillating bolometers. The detector, consisting of 24 enriched and 2 natural ZnSe crystals, has been taking data at Laboratori Nazionali del Gran Sasso from March 2017 to December 2018 (Phase I) and from May 2019 to February 2020 (Phase II), for a total exposure of 16.59 kg × yr of ZnSe. In this contribution, we present the new combined results of Phase-I and Phase II in the search for Se-82 0νDBD, both to the ground state and to the excited states of Kr-82. The successful operation of the CUPID-0 detector demonstrates that scintillating calorimeters allow us to reach the lowest background for calorimetric experiments: (3.5 +/- 1.0) × 10^(-3) counts/(keV kg yr). We reach a 90% credible interval median sensitivity of 0.7 × 10^25 yr and set the most stringent limit on the half-life of Se-82 0vDBD, T1/2 > 4.7 x 10^24 yr (90% credible interval), corresponding to mββ < (276 - 570) meV depending on the nuclear matrix element calculations. The CUPID-0 result surpasses the sensitivity foreseen for scheduled Se82-based experiments, and it is therefore a candidate to be the best result on the Se-82 for a long time.