We review the calculations 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 computational framework MATRIX, which has been publicly released recently. Our calculations include the leptonic decays of W and Z bosons, consistently taking into account spin correlations, off-shell effects and non-resonant contributions. We present inclusive cross section for the production of massive vector-boson pairs, 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 show some examples 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.