We consider ZZ production in hadronic collisions and present state-of-the-art predictions in QCD perturbation theory matched to parton showers. Next-to-next-to-leading order corrections to the quark-initiated channel are combined with parton showers using the MiNNLOPS method, while next-to-leading order corrections to the loop-induced gluon fusion channel are matched using the Powheg method. Their combination, dubbed nNNLO+PS, constitutes the best theoretical description of ZZ events to date. Spin correlations, interferences and off-shell effects are included by calculating the full process pp → ℓ+ℓ−ℓ(′)+ℓ(′)−. We show the crucial impact of higher-order corrections for both quark- and gluon-initiated processes as well as the relevance of the parton shower in certain kinematical regimes. Our predictions are in very good agreement with recent LHC data.