CUORE is the first bolometric tonne-scale experiment aiming at the investigation of neutrinoless double-beta (0$\nu$2$\beta$) decay of $^{130}$Te. The cryogenic commissioning followed by the detector installation and cool down took place during 2016. After the optimisation of all the detectors, the data-taking started in spring 2017. We report about the results of the first dataset acquired in May, which led to a limit on the 0$\nu$2$\beta$ half-life of $^{130}$Te of 6.6$\times$10$^{24}$ yr. An upgrade of CUORE, named CUPID, is planned to improve the 0$\nu$2$\beta$-decay sensitivity via passive and active background reduction and crystal enrichment. Some technologies for CUPID are currently under study and two of them are presented here, involving the detection of Cherenkov and scintillation light emitted by enriched $^{130}$TeO$_2$ and Li$^{100}_2$MoO$_4$ crystals respectively. This will allow us to reject the currently dominant a background.