  Apart from the well-known NNLO QCD and NLO electroweak corrections to W- and
Z-boson production at hadron colliders, the most important fixed-order
corrections are given by the mixed QCD-electroweak corrections of
$\mathcal{O}(\alpha_s\alpha)$. The knowledge of these corrections is of
particular importance to control the theoretical uncertainties in the upcoming
high-precision measurements of the W-boson mass and the effective weak mixing
angle at the LHC. Since these observables are dominated by the phase-space
regions of resonant W/Z bosons, we address the $\mathcal{O}(\alpha_s\alpha)$
corrections in the framework of an expansion about the W/Z poles. Retaining
only the leading, resonant contribution in the so-called pole approximation,
the corrections can be classified into factorizable and non-factorizable
contributions. In this article we review our calculation of the numerically
dominant corrections which arise from factorizable corrections of
"initial-final" type, i.e. they combine the QCD corrections to the production
with the large electroweak corrections to the decay of the W/Z boson. Moreover,
we compare our results to simpler approximate combinations of electroweak and
QCD corrections based on naive products of NLO QCD and electroweak correction
factors and using leading-logarithmic approximations for QED final-state
radiation. Finally, we estimate the shift in the W-boson mass that results from
the $\mathcal{O}(\alpha_s\alpha)$ corrections to the transverse-mass
distribution.
