The LHC Higgs Cross Section Working Group's 2012 and 2013 report summarizes the state of Higgs physics at the LHC, focusing on Standard Model (SM) and beyond-the-Standard-Model (BSM) predictions. The report builds on previous work and provides refined predictions for Higgs phenomenology around the experimentally observed mass of 125–126 GeV, as well as for heavy SM-like Higgs bosons and the Minimal Supersymmetric Standard Model (MSSM). It also addresses the extraction of Higgs properties such as couplings, spin, and CP-parity. The report includes detailed calculations of branching ratios, differential cross sections, and theoretical uncertainties, with a focus on the Higgs production and decay processes. It discusses the impact of next-to-leading order (NLO) corrections and interference effects in various decay channels, such as H → WW/ZZ → 4f, and presents results for the Higgs boson mass, decay widths, and branching ratios. The report also addresses the treatment of theoretical uncertainties, particularly those arising from QCD scale and PDF+αs, and provides a comprehensive overview of Monte Carlo generators and their application in Higgs physics. The report emphasizes the importance of precise measurements and the need for further theoretical and experimental efforts to determine the nature of the newly discovered Higgs-like particle.The LHC Higgs Cross Section Working Group's 2012 and 2013 report summarizes the state of Higgs physics at the LHC, focusing on Standard Model (SM) and beyond-the-Standard-Model (BSM) predictions. The report builds on previous work and provides refined predictions for Higgs phenomenology around the experimentally observed mass of 125–126 GeV, as well as for heavy SM-like Higgs bosons and the Minimal Supersymmetric Standard Model (MSSM). It also addresses the extraction of Higgs properties such as couplings, spin, and CP-parity. The report includes detailed calculations of branching ratios, differential cross sections, and theoretical uncertainties, with a focus on the Higgs production and decay processes. It discusses the impact of next-to-leading order (NLO) corrections and interference effects in various decay channels, such as H → WW/ZZ → 4f, and presents results for the Higgs boson mass, decay widths, and branching ratios. The report also addresses the treatment of theoretical uncertainties, particularly those arising from QCD scale and PDF+αs, and provides a comprehensive overview of Monte Carlo generators and their application in Higgs physics. The report emphasizes the importance of precise measurements and the need for further theoretical and experimental efforts to determine the nature of the newly discovered Higgs-like particle.