  We consider QCD corrections to Higgs boson production through gluon--gluon
fusion in hadron collisions. We compute the cross section, performing the
all-order resummation of multiple soft-gluon emission at
next-to-next-to-leading logarithmic level. Known fixed-order results (up to
next-to-next-to-leading order) are consistently included in our calculation. We
give phenomenological predictions for Higgs boson production at the Tevatron
and at the LHC. We estimate the residual theoretical uncertainty from
perturbative QCD contributions. We also quantify the differences obtained by
using the presently available sets of parton distributions.
