The Higgs-boson production cross section at $\mathrm{pp}$ and $p\overline{p}$ colliders is calculated in QCD at next-to-next-to-leading order (NNLO). We find that the perturbative expansion of the production cross section is well behaved and that scale dependence is reduced relative to the NLO result. These findings give us confidence in the reliability of the prediction. We also report an error in the NNLO correction to Drell-Yan production.

We implement, at next-to-next-to-leading order, the QCD corrections to Standard Model Higgs boson production in association with vector bosons at hadron colliders, $q\bar{q} \to HV$ with $V=W,Z$. They consist of the two--loop corrections to the Drell--Yan process for the production of off-shell vector bosons, $q\bar{q} \to V^*$, and in the case of $Z$ final states, of the additional contribution from heavy-quark loop mediated processes, in particular $gg \to HZ$. For the Higgs boson masses relevant at the Tevatron and the LHC, $M_H \lsim 200$--300 GeV, the two-loop corrections are small, increasing the production cross sections by less than 5% and 10%, respectively; the scale dependence is reduced to a level of less than a few per cent. This places these processes among the most theoretically clean Higgs boson production channels at hadron colliders.

The total cross section for Higgs boson production in bottom-quark annihilation is evaluated at next-to-next-to-leading order in QCD. This is the first time that all terms at order ${\alpha }_s^2$ are taken into account. We find a greatly reduced scale dependence with respect to lower order results, for both the factorization and the renormalization scales. The behavior of the result is consistent with earlier determinations of the appropriate factorization scale for this process of ${\mu }_F\approx M_H/4,$ and supports the validity of the bottom parton density approach for computing the total inclusive rate. We present precise predictions for the cross section at the Fermilab Tevatron and the CERN Large Hadron Collider.