  We consider the transverse-momentum ($q_T$) distribution of Drell-Yan lepton
pairs produced, via $W$ and $Z/\gamma^*$ decay, in hadronic collisions. At
small values of $q_T$, we resum the logarithmically-enhanced perturbative QCD
contributions up to next-to-next-to-leading logarithmic accuracy. Resummed
results are consistently combined with the known ${\mathcal O}(\alpha_S^2)$
fixed-order results at intermediate and large values of $q_T$. Our calculation
includes the leptonic decay of the vector boson with the corresponding spin
correlations, the finite-width effects and the full dependence on the
final-state lepton(s) kinematics. The computation is encoded in the numerical
program DYRes, which allows the user to apply arbitrary kinematical cuts on the
final-state leptons and to compute the corresponding distributions in the form
of bin histograms. We present a comparison of our results with some of the
available LHC data. The inclusion of the leptonic decay in the resummed
calculation requires a theoretical discussion on the $q_T$ recoil due to the
transverse momentum of the produced vector boson. We present a $q_T$ recoil
procedure that is directly applicable to $q_T$ resummed calculations for
generic production processes of high-mass systems in hadron collisions.
