The paper presents the latest developments of the MadGraph/MadEvent Monte Carlo event generator, focusing on its applications to hadron collider physics. The new version of the generator allows for the direct generation of events at the parton, hadron, and detector levels through a web interface for various processes in the Standard Model and beyond (HEFT, MSSM, 2HDM). Key additions include a framework for implementing user-defined new physics models, standalone running mode for matrix element creation and testing, event generation for different processes in the same run, and two data analysis platforms. The paper also discusses the matching of jet production by parton showers and matrix elements, and provides several examples of applications, such as Higgs search, Higgs CP properties, spin of a new resonance, single-top and Higgs associated production, strong SUSY pair production, and inclusive $W+$jets matched samples. The new features and capabilities of the MadGraph/MadEvent package are illustrated through these applications, highlighting its utility in both theoretical and experimental physics research.The paper presents the latest developments of the MadGraph/MadEvent Monte Carlo event generator, focusing on its applications to hadron collider physics. The new version of the generator allows for the direct generation of events at the parton, hadron, and detector levels through a web interface for various processes in the Standard Model and beyond (HEFT, MSSM, 2HDM). Key additions include a framework for implementing user-defined new physics models, standalone running mode for matrix element creation and testing, event generation for different processes in the same run, and two data analysis platforms. The paper also discusses the matching of jet production by parton showers and matrix elements, and provides several examples of applications, such as Higgs search, Higgs CP properties, spin of a new resonance, single-top and Higgs associated production, strong SUSY pair production, and inclusive $W+$jets matched samples. The new features and capabilities of the MadGraph/MadEvent package are illustrated through these applications, highlighting its utility in both theoretical and experimental physics research.