  This talk summarizes the first calculation of the next-to-leading-order
electroweak corrections to W-boson + jet hadroproduction including leptonic
W-boson decays [1]. The W-boson resonance is treated consistently using the
complex-mass scheme, and all off-shell effects are taken into account. The
corresponding next-to-leading-order QCD corrections have also been
recalculated. All the results are implemented in a flexible Monte Carlo code.
Selected numerical results for this Standard Model benchmark process are
presented for the LHC.
