  The next-to-leading order (NLO) QCD radiative corrections to W+W- production
at hadron colliders are well understood. We combine NLO perturbative QCD
calculations with soft-gluon resummation of threshold logarithms to find a
next-to-next-to leading logarithmic (NNLL) prediction for the total cross
section and the invariant mass distribution at the LHC. We also obtain
approximate next-to-next-to-leading order (NNLO) results for the total W+W-
cross section at the LHC which includes all contributions from the scale
dependent leading singular terms. Our result for the approximate NNLO total
cross section is the most precise theoretical prediction available.
Uncertainties due to scale variation are shown to be small when the threshold
logarithms are included. NNLL threshold resummation increases the W+W-
invariant mass distribution by ~ 3-4% in the peak region for both \sqrt{S}=8
and 14 TeV. The NNLL threshold resummed and approximate NNLO cross sections
increase the NLO cross section by 0.5-3% for \sqrt{S}=7, 8, 13, and 14 TeV.
