Radiative MHD Simulations of Sunspot Structure—Challenges and recent developments

For a long time 3D radiative MHD simulations of sunspots were out of reach. With increasing computing power there has been recently substantial progress in modeling magneto‐convection in strong magnetic field regions and complete sunspots including the transition from umbra toward plage like solar granulation. 3D simulations point toward a unified understanding of sunspot fine structure in terms of a magneto convection process in a background field with varying inclination angle. We summarize here briefly the most recent developments.