  We consider the transverse-momentum ($q_T$) distribution of $Z$ bosons
produced in hadronic collisions. At small values of $q_T$, we perform the
analytic resummation of the logarithmically enhanced QED contributions up to
next-to-leading logarithmic accuracy, including the mixed QCD-QED contributions
at leading logarithmic accuracy. Resummed results are consistently matched with
the next-to-leading fixed-order results (i.e. $\mathcal{O}(\alpha^2)$) at
small, intermediate and large values of $q_T$. We combine the QED corrections
with the known QCD results at next-to-next-to-leading order
($\mathcal{O}(\alpha_S^2)$) and next-to-next-to-leading logarithmic accuracy.
We show numerical results at LHC and Tevatron energies, studying the impact of
the QED corrections and providing an estimate of the corresponding perturbative
uncertainty. Our analytic results for the combined QED and QCD resummation,
obtained through an extension of the $q_T$ resummation formalism in QCD, are
valid for the production of generic neutral and colourless high-mass systems in
hadronic collision.
