  Electroweak gauge boson pair production is one of the most important Standard
Model processes at the LHC, not only because it is a benchmark process but also
by its ability to probe the electroweak interaction directly. We present full
next-to-leading order predictions for the production cross sections and
distributions of on-shell massive gauge boson pair production in the Standard
Model. This includes the QCD and electroweak (EW) corrections. We study the
hierarchy between the different channels when looking at the size of the QCD
gluon-induced processes and the EW photon-induced processes and provide the
first comprehensive explanation of this hierarchy thanks to analytical
leading-logarithmic results. We also provide a detailed study of the
theoretical uncertainties affecting the total cross section predictions that
stem from scale variation, parton distribution function and $\alpha_s$ errors.
We then compare with the present LHC data.
