  The Drell-Yan process at hadron colliders is a fundamental benchmark for the
study of strong interactions and the extraction of electro-weak parameters. The
outstanding precision of the LHC demands very accurate theoretical predictions
with a full account of fiducial experimental cuts. In this letter we present a
state-of-the-art calculation of the fiducial cross section and of differential
distributions for this process at third order in the strict fixed-order
expansion in the strong coupling, as well as including the all-order
resummation of logarithmic corrections. Together with these results, we present
a detailed study of the subtraction technique used to carry out the calculation
for different sets of experimental cuts, as well as of the sensitivity of the
fiducial cross section to infrared physics. We find that residual theory
uncertainties are reduced to the percent level and that the robustness of the
predictions can be improved by a suitable adjustment of fiducial cuts.
