Numerical simulations of the Earth System are used for global climate modeling, regional climate modeling, and numerical weather prediction. Over time, these models are evolving to include increased complexity, higher resolution, multi-scale features, advanced time-stepping techniques, and improved performance on next-generation massively parallel supercomputers. Such changes are needed to answer pressing questions related to climate change and the incidence of extreme events. This session encompasses the development and application of advanced numerical techniques for both resolved dynamics and subgrid-scale physical parameterizations in Earth System models.