  We present results of the first calculation of next-to-leading-order
electroweak corrections to W-boson pair production at the LHC that fully takes
into account leptonic W-boson decays and off-shell effects. Employing realistic
event selections, we discuss the corrections in situations that are typical for
the study of W-boson pairs as a signal process or of Higgs-boson decays $H\to W
W^*$, to which W-boson pair production represents an irreducible background. In
particular, we compare the full off-shell results, obtained treating the
W-boson resonances in the complex-mass scheme, to previous results in the
so-called double-pole approximation, which is based on an expansion of the loop
amplitudes about the W resonance poles. At small and intermediate scales, i.e.
in particular in angular and rapidity distributions, the two approaches show
the expected agreement at the level of fractions of a percent, but larger
differences appear in the TeV range. For transverse-momentum distributions, the
differences can even exceed the 10% level in the TeV range where "background
diagrams" with one instead of two resonant W bosons gain in importance because
of recoil effects.
