  We present the first computation of the full next-to-leading-order QCD and
electroweak corrections to the WZ scattering process at the LHC. All off-shell,
gauge-boson-decay, and interference effects are taken into account for the
process $\mathrm{p} \mathrm{p} \to \mu^+\mu^-\mathrm{e}^+\nu_\mathrm{e}
\mathrm{j} \mathrm{j} + X$ at the orders $\mathcal{O}{\left( \alpha_\mathrm{s}
\alpha^6 \right)}$ and $\mathcal{O}{\left( \alpha^7 \right)}$. The electroweak
corrections feature the typical Sudakov behaviour towards high energy and
amount to $-16\%$ relative to the electroweak contribution to the integrated
cross section. Moreover, the corrections induce significant shape distortions
in differential distributions. The next-to-leading-order analysis of the quark-
and gluon-induced channels is supplemented by a leading-order study of all
possible contributions to the full $4\ell+2\mbox{jets}$ production cross
section in a realistic fiducial phase-space volume.
