Abstract　 　　
　 AGN feedback plays an important role in cosmic structure evolution and is one of the central unsolved problems in current astronomy. The most compelling evidence for AGN feedback comes from numerous detections of X-ray-deficient cavities in galaxy clusters, apparently evolved from the interaction of AGN radio jets with the intracluster medium. In this talk, I will present my recent theoretical and numerical work on the physics, impact, and triggering mechanisms of AGN mechanical feedback in galaxy clusters. I will also discuss our AGN-jet model for the recently-discovered Fermi gamma-ray bubbles in the Milky Way, which shows that the Fermi bubbles could be produced by a pair of powerful jets released from Sgr A*, the supermassive black hole at the Galactic Center, about 1-3 million years ago. I will end my talk with a list of unsolved mysteries of AGN feedback and the Fermi bubbles.