Galaxy clusters are the largest virialized structures in our Universe, which contains massive dark matter halos and very hot intracluster medium (ICM). Generally speaking, galaxy clusters evolve in a self-similar way. But there are two main processes that could break the self-similarity of galaxy clusters, i.e. active galactic nucleus (AGN) feedback and cluster mergers. In this talk, I will discuss the effects of these two processes on the formation of galaxy clusters. In the cluster center, X-ray bubbles are inflated by the powerful jets and buoyantly rise outwards. Internal waves excited by these buoyant bubbles may play a very important role in heating the ICM. On the other hand, cluster mergers could re-distribute the matter in galaxy clusters on the Mpc scale. Shock fronts and contact discontinuities are naturally formed during this supersonic process. Our study shows that the merger shock could detach from the gas halo which drives it and travels to the large cluster radius. A "habitable zone" populated by the runaway merger shocks may exist in cluster outskirts, where the shock strength can be maintained or even amplifi ed.
