  We consider the production of $W\gamma$ and $Z\gamma$ pairs at hadron
colliders. We report on the complete fully differential computation of
radiative corrections at next-to-next-to-leading order (NNLO) in QCD
perturbation theory. The calculation includes the leptonic decay of the vector
boson with the corresponding spin correlations, off shell effects and
final-state photon radiation. We present numerical results for $pp$ collisions
at 7 and 8 TeV and we compare them with available LHC data. In the case of
$Z\gamma$ production, the impact of NNLO corrections is generally moderate,
ranging from 8% to 18%, depending on the applied cuts. In the case of $W\gamma$
production, the NNLO effects are more important, and range from 19% to 26%,
thereby improving the agreement of the theoretical predictions with the data.
As expected, the impact of QCD radiative corrections is significantly reduced
when a jet veto is applied.
