  We consider $W^+W^-$ production in hadronic collisions and present the
computation of next-to-next-to-leading order accurate predictions consistently
matched to parton showers (NNLO+PS) using the MiNNLO$_{\rm PS}$ method. Spin
correlations, interferences and off-shell effects are included by calculating
the full process $pp \to e^+\nu_e \mu^-\bar{\nu}_\mu$. This is the first
NNLO+PS calculation for $W^+W^-$ production that does not require an
a-posteriori multi-differential reweighting. The evaluation time of the
two-loop contribution has been reduced by more than one order of magnitude
through a four-dimensional cubic spline interpolation. We find good agreement
with the inclusive and fiducial cross sections measured by ATLAS and CMS. Both
NNLO corrections and matching to parton showers are important for an accurate
simulation of the $W^+W^-$ signal, and their matching provides the best
description of fully exclusive $W^+W^-$ events to date.
