  A convincing observation of neutrino-less double beta decay (0$\nu$DBD)
relies on the possibility of operating high energy-resolution detectors in
background-free conditions. Scintillating cryogenic calorimeters are one of the
most promising tools to fulfill the requirements for a next-generation
experiment. Several steps have been taken to demonstrate the maturity of this
technique, starting from the successful experience of CUPID-0. The CUPID-0
experiment demonstrated the complete rejection of the dominant alpha background
measuring the lowest counting rate in the region of interest for this
technique. Furthermore, the most stringent limit on the $^{82}$Se 0$\nu$DBD was
established running 26 ZnSe crystals during two years of continuous detector
operation. In this contribution we present the final results of CUPID-0 Phase I
including a detailed model of the background, the measurement of the $^{82}$Se
2$\nu$DBD half-life and the evidence that this nuclear transition is single
state dominated.
