In this talk we cover the current status of the calculation of
mixed \QCDxEW corrections to the Drell-Yan process at the LHC.
After briefly reviewing ongoing efforts in the computation
of the fully off-shell case,
we will focus on the scenario where an electroweak vector boson
is resonant.

In this respect, complete $\mathcal{O}(\alpha\alpha_s)$ predictions
for the production of on-shell $Z$ and $W$ bosons at the LHC recently became
available in literature.
As a case study, we present results for the inclusive and
fiducial cross sections as well as kinematic distributions
for the production of a $Z$ boson.
We discuss the impact of these corrections and describe their salient features.