The production of boson pairs is a very important class of processes at hadron colliders, both for validation of the Standard Model and as
background to New Physics. I report on the fully exclusive computation of this process class at next-to-next-to-leading order (NNLO) in QCD perturbation theory by means of the qT-subtraction method. This method, which is applicable to achieve NNLO QCD accuracy in the production of any colourless final-state, is introduced, and the technical realization of the calculation within the publicly available MATRIX framework is discussed.
I present some numerical results and comparisons to experimental data on cross sections and selected differential distributions for the production of ZZ, WW and WZ pairs in their leptonic decay modes. Finally, I will briefly address ongoing extensions of the MATRIX framework towards NLO EW corrections, leading N3LO QCD contributions and resummation of the transverse momentum of the colourless system.