  We consider QCD corrections to Higgs boson production through gluon-gluon
fusion in hadron collisions. Using the recently evaluated two-loop amplitude
for this process and the corresponding factorization formulae for soft-gluon
bremsstrahlung at O(alpha_s^2), we compute the soft and virtual contributions
to the NNLO cross section. We also discuss soft-gluon resummation at
next-to-next-to-leading logarithmic accuracy. Numerical results for Higgs boson
production at the LHC are presented.
