  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 MiNNLO$_{\text{PS}}$ 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 $pp \to
\ell^+\ell^-\ell^{(\prime)+}\ell^{(\prime)-}$. 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.
