Feedback from active galactic nuclei (AGN) is one of the most important processes governing the formation and evolution of galaxies and galaxy clusters. It is believed to be responsible for inhibiting the formation of massive galaxies and for solving the long-standing "cooling-flow problem" in galaxy clusters. A lot of understanding of AGN feedback has been gained using hydrodynamic simulations; however, some of the relevant physical processes are unresolvable or not captured by pure hydrodynamics, such as plasma effects and cosmic-ray (CR) physics. In this talk, I will present how we use simulations that incorporate this "microphysics" to understand how AGN jets feedback on galactic and cluster scales. Specifically, I will discuss our recent progress on the understanding of AGN heating in clusters, and how this heating depends on the microphysical transport processes including anisotropic conduction, anisotropic viscosity and CR streaming. I will also talk about how we could use multi-messenger observations of the Fermi bubbles as a nearby laboratory for studying AGN feedback. Finally, I will conclude with open questions and future prospects of applying simulations beyond hydrodynamics to various interesting astrophysical systems.