Recent theoretical progress in the evaluation of Higgs boson production at the LHC within the Standard Model (SM) and its minimal supersymmetric extension (MSSM) is reviewed. The paper discusses two-loop QCD corrections to squark loop contributions to scalar Higgs production in the MSSM and soft gluon resummation effects in Standard and SUSY Higgs production via the gluon fusion mechanism. The dominant Higgs production mechanism at the LHC is the gluon fusion process $ qg \rightarrow H $, mediated by a heavy quark triangle loop at lowest order. Two-loop QCD corrections have been calculated, resulting in a significant increase of the predicted total cross section by about 50–100%. These corrections reduce the dependence on the unphysical renormalization and factorization scales, resulting in an estimate of about 15% for the remaining scale sensitivity. The NLO corrections are dominated by soft gluon radiation effects. The MSSM requires the introduction of two Higgs doublets, leading to five scalar Higgs particles: two scalar CP-even $ h, H $, one pseudoscalar CP-odd $ A $, and two charged bosons $ H^{\pm} $. The mass of the lightest scalar Higgs particle $ h $ is restricted to be smaller than $ \sim 130~GeV $, while the direct search at LEP1 sets lower bounds of about 45 GeV on the masses of the MSSM Higgs bosons. The dominant neutral Higgs production mechanisms at the LHC are the gluon fusion processes $ gg \rightarrow h, H, A $ and Higgs-strahlung off bottom quarks, which become important only for large $ \tan\beta $. The coupling of the neutral Higgs particles to gluons is mediated by top and bottom loops, with the latter providing the dominant contribution for large $ \tan\beta $, and squark loops, if their masses are smaller than about 400 GeV. The two-loop (NLO) QCD corrections to the quark loop contributions to the gluon fusion mechanism have also been calculated, and conclusions analogous to the SM case emerge. Soft gluon radiation effects again provide the dominant contribution to these corrections, for small $ \tan\beta $. Recent calculations of QCD corrections to the squark loop contributions to the cross sections $ \sigma(pp \to \mathcal{H} + X) $ of the fusion processes for the neutral CP-even Higgs particles $ H = h, H $ have been performed. Because of CP invariance, squark loops do not contribute to the production of the CP-odd Higgs boson in lowest order. The QCD corrections from squark loops were evaluated in the heavy squark limit, where the calculation can be simplified by extending the lowest-order low-energy theorems to two loops. This limit shouldRecent theoretical progress in the evaluation of Higgs boson production at the LHC within the Standard Model (SM) and its minimal supersymmetric extension (MSSM) is reviewed. The paper discusses two-loop QCD corrections to squark loop contributions to scalar Higgs production in the MSSM and soft gluon resummation effects in Standard and SUSY Higgs production via the gluon fusion mechanism. The dominant Higgs production mechanism at the LHC is the gluon fusion process $ qg \rightarrow H $, mediated by a heavy quark triangle loop at lowest order. Two-loop QCD corrections have been calculated, resulting in a significant increase of the predicted total cross section by about 50–100%. These corrections reduce the dependence on the unphysical renormalization and factorization scales, resulting in an estimate of about 15% for the remaining scale sensitivity. The NLO corrections are dominated by soft gluon radiation effects. The MSSM requires the introduction of two Higgs doublets, leading to five scalar Higgs particles: two scalar CP-even $ h, H $, one pseudoscalar CP-odd $ A $, and two charged bosons $ H^{\pm} $. The mass of the lightest scalar Higgs particle $ h $ is restricted to be smaller than $ \sim 130~GeV $, while the direct search at LEP1 sets lower bounds of about 45 GeV on the masses of the MSSM Higgs bosons. The dominant neutral Higgs production mechanisms at the LHC are the gluon fusion processes $ gg \rightarrow h, H, A $ and Higgs-strahlung off bottom quarks, which become important only for large $ \tan\beta $. The coupling of the neutral Higgs particles to gluons is mediated by top and bottom loops, with the latter providing the dominant contribution for large $ \tan\beta $, and squark loops, if their masses are smaller than about 400 GeV. The two-loop (NLO) QCD corrections to the quark loop contributions to the gluon fusion mechanism have also been calculated, and conclusions analogous to the SM case emerge. Soft gluon radiation effects again provide the dominant contribution to these corrections, for small $ \tan\beta $. Recent calculations of QCD corrections to the squark loop contributions to the cross sections $ \sigma(pp \to \mathcal{H} + X) $ of the fusion processes for the neutral CP-even Higgs particles $ H = h, H $ have been performed. Because of CP invariance, squark loops do not contribute to the production of the CP-odd Higgs boson in lowest order. The QCD corrections from squark loops were evaluated in the heavy squark limit, where the calculation can be simplified by extending the lowest-order low-energy theorems to two loops. This limit should