The paper reviews recent theoretical advancements in evaluating Higgs boson production at the Large Hadron Collider (LHC) within the Standard Model (SM) and its minimal supersymmetric extension (MSSM). Key topics include: 1. **Two-loop QCD Corrections**: The paper discusses the two-loop QCD corrections to squark loop contributions in scalar Higgs production in the MSSM, which significantly increase the predicted total cross section by 50–100%. These corrections are dominated by soft gluon radiation effects. 2. **Soft Gluon Resummation**: The effects of soft gluon resummation in Higgs boson production via gluon fusion are explored. The resummation is performed using methods similar to those used for the Drell-Yan process, leading to a quantitative estimate of NNLO corrections to the gluon-fusion mechanism. 3. **Squark Loops**: The impact of squark loops on the production of CP-even Higgs particles (h and H) is analyzed. The QCD corrections from squark loops are large, enhancing the cross sections by a factor of 1.6 to 2.8. However, the inclusion of squark loops does not substantially modify the $K$-factors compared to the case without squark loops. 4. **Scale Dependence**: The paper examines the scale dependence of the Higgs production cross section at leading order (LO), next-to-leading order (NLO), and next-to-next-to-leading order (NNLO). The results show a strong stabilization of the scale dependence at NNLO, indicating the potential for more accurate predictions with NNLO parton densities. 5. **Physical Predictions**: The paper discusses the challenges in making physical predictions at NNLO due to the lack of NNLO parton densities and the need to regularize infrared renormalon singularities. The author acknowledges the organizers and collaborators for their contributions to the work presented.The paper reviews recent theoretical advancements in evaluating Higgs boson production at the Large Hadron Collider (LHC) within the Standard Model (SM) and its minimal supersymmetric extension (MSSM). Key topics include: 1. **Two-loop QCD Corrections**: The paper discusses the two-loop QCD corrections to squark loop contributions in scalar Higgs production in the MSSM, which significantly increase the predicted total cross section by 50–100%. These corrections are dominated by soft gluon radiation effects. 2. **Soft Gluon Resummation**: The effects of soft gluon resummation in Higgs boson production via gluon fusion are explored. The resummation is performed using methods similar to those used for the Drell-Yan process, leading to a quantitative estimate of NNLO corrections to the gluon-fusion mechanism. 3. **Squark Loops**: The impact of squark loops on the production of CP-even Higgs particles (h and H) is analyzed. The QCD corrections from squark loops are large, enhancing the cross sections by a factor of 1.6 to 2.8. However, the inclusion of squark loops does not substantially modify the $K$-factors compared to the case without squark loops. 4. **Scale Dependence**: The paper examines the scale dependence of the Higgs production cross section at leading order (LO), next-to-leading order (NLO), and next-to-next-to-leading order (NNLO). The results show a strong stabilization of the scale dependence at NNLO, indicating the potential for more accurate predictions with NNLO parton densities. 5. **Physical Predictions**: The paper discusses the challenges in making physical predictions at NNLO due to the lack of NNLO parton densities and the need to regularize infrared renormalon singularities. The author acknowledges the organizers and collaborators for their contributions to the work presented.