Vector-boson production at the LHC: QCD and electroweak effects

A profound understanding of vector-boson production processes is of crucial importance at the LHC. The corresponding cross sections are large, and the final states are easy to reconstruct due to the clean signatures in the leptonic decay modes. Therefore, such processes play an important role as backgrounds in a large variety of new-physics signals, and they may furthermore help to better understand the well-established Standard-Model physics in a hadron-collider environment. We review the recent progress in the theoretical description of higher-order QCD and electroweak effects in vector-boson production at the LHC, discussing the Drell--Yan process, vector-boson pair production and vector-boson production with associated jets.