We report on a recent calculation of next-to-leading-order (NLO) QCD and electroweak
corrections to like-sign W-boson scattering at the Large Hadron Collider, including all
partonic channels and W-boson decays in the process
$pp \to e^+ \nu_e \mu^+ \nu_\mu jj + X$.
The calculation is implemented in the Monte Carlo integrator Bonsay and
comprises the full tower of NLO contributions of the orders
$\alpha_s^3\alpha^4$, $\alpha_s^2\alpha^5$,
$\alpha_s\alpha^6$, and $\alpha^7$.
Our numerical results confirm and extend previous results, in particular the occurrence
of large purely electroweak corrections of the order of
$\sim-12\%$ for integrated cross sections,
which get even larger in distributions.
We construct a "VBS approximation'' for the NLO prediction based on
partonic channels and gauge-invariant (sub)matrix elements potentially containing the
vector-boson scattering (VBS) subprocess and on resonance expansions of the W decays.
The VBS approximation reproduces the full NLO predictions within $\sim1.5\%$
in the most important regions of phase space.
Moreover, we discuss results from different versions of
"effective vector-boson approximations''
at leading order, based on the collinear emission of W bosons of incoming (anti)quarks.
However, owing to the only mild collinear enhancement and the design of VBS analysis cuts,
the quality of this approximation turns out to be only qualitative at the LHC.