| Description: | Over the last two decades, general relativistic magnetohydrodynamic simulations (GRMHD) have drawn a robust theoretical picture of jet formation in low-luminosity sources. The observations by the Event Horizon Telescope now allow to test these theories at an unprecedented level. I will take this opportunity to review the state-of-the-art in 3D numerical source models. Nowadays, adaptive mesh refinement simulations resolve the black hole engine as well as the jet outflow over several decades. To demonstrate how results compare between different codes, I will also report on the first comprehensive GRMHD code comparison effort of black hole accretion carried out by the community. As example applications, first conclusions drawn from the GRMHD simulation library which was applied to the 2017 EHT observations will be discussed and I will show extensions of the modeling towards inclusion of non-thermal particles and more exotic compact objects.
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