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LLNL has developed a family of magnetic flux compression generators used in high explosive pulsed power experiments. The three types of generators used in these experiments are coaxial, helical and flat plate designs. Modeling and simulation played a critical role during the development of these generators, and continues to be used extensively as experiments are fielded. With experimental peak current magnitudes ranging from mega-amperes to 100 mega-amperes, and peak power levels up to 13 terawatts, all aspects of these generators are dynamic. Consequently, LLNL has applied some of the most advanced codes to the problem of modeling and simulating magnetic flux compression generators. For the coaxial and flat plate geometries, CALE, a 2D MHD code, and ALE3D, a 2D/3D MHD code, have been utilized. For the helical generators, CAGEN, a commercial helical modeling code, is employed, along with input from CALE or ALE3D. Also, preliminary efforts to model a helical geometry in ALE3D have resulted in full 3D MHD simulations of helical flux compression generators. As a result of the application of these codes, excellent agreement with experimental data and unprecedented insight into coaxial, helical, and flat plate generator operation has been achieved. This paper gives an overview of the advanced modeling and simulation methods applied to magnetic flux compression generators at LLNL. Comparisons of simulation and experimental data will be given, along with various aspects of the designs which were analyzed through these modeling capabilities.