  We give an overview of our calculation of the next-to-next-to-leading order
(NNLO) QCD corrections to W + jet production in hadronic collisions.
Phenomenological results for multiple differential distributions are compared
to CMS data for 8 TeV proton-proton collisions. We further discuss the
application of the calculation to the transverse momentum spectrum of inclusive
W boson production, again accompanied by a comparison to 8 TeV CMS data. In
both cases, the inclusion of NNLO QCD effects give an improved agreement
between theory and data with considerably reduced scale uncertainties with
respect to the next-to-leading order (NLO) results.
