We review the computations of the next-to-next-to-leading order (NNLO) QCD corrections to vector-boson pair production processes in proton–proton collisions and their implementation in the numerical code MATRIX. Our calculations include the leptonic decays of W and Z bosons, consistently taking into account all spin correlations, off-shell effects and non-resonant contributions. For massive vector-boson pairs we show inclusive cross sections, applying the respective mass windows chosen by ATLAS and CMS to define Z bosons from their leptonic decay products, as well as total cross sections for stable bosons. Moreover, we provide samples of differential
distributions in fiducial phase-space regions inspired by typical selection cuts used by the LHC experiments. For the vast majority of measurements, the inclusion of NNLO corrections significantly improves the agreement of the Standard Model predictions with data.