I will discuss recent achievements in theoretical and numerical models of stellar and black hole feedback in galaxies and galaxy clusters. In this talk, I will also emphasize the existence of open problems that were identified in recent theoretical and numerical studies. Some of the problems related to stellar feedback are likely to be solved with the current and next generation of numerical simulations aimed at simulating the detail physics of specific feedback processes. However, challenges regarding black hole feedback will require significantly more involvement from the theoretical and observational community before being completely overcome.