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The pair production of massive vector bosons at the LHC is among the most studied SM processes, both as a signal on its own and as a background to BSM physics and Higgs searches. In this context, precise theoretical predictions for diboson production are mandatory. I will discuss the first calculation of the NLO QCD+NLO EW corrections to diboson production processes consistently matched to both QED and QCD parton showers in the POWHEG-BOX framework.