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Supernovae and their progenitor stars are in many aspects still poorly understood. While time-implicit hydrostatic codes are an invaluable tool with which to study the long term evolution of stars, they necessarily rely on the assumption of spherical symmetry and approximations for dynamic processes like convection. I will give an overview of approaches to modelling stellar interiors and the current status and direction of the field. Then, I will focus on the specific challenges of simulating the evolution of massive and intermediate-mass stars, which are the progenitors of core-collapse and electron-capture supernovae, respectively. These include multidimensional hydrodynamic simulations of turbulent deflagrations and convection coupled with nuclear reaction networks. Host: Chris Neale |