Supermassive black holes (SMBHs) have been found to be ubiquitous in the nuclei of early-type galaxies and of bulges of spirals. There are evidences of a tight correlation between the SMBH masses, the velocity dispersions of stars in the spheroidal components galaxies and other galaxy properties. Also the evolution of the luminosity density due to nuclear activity is similar to that due to star formation. All that suggests an evolutionary connection between Active Galactic Nuclei (AGNs) and their host galaxies. After a review of these evidences this lecture discusses how AGNs can affect the host galaxies. Other feedback processes advocated to account for the differences between the halo and the stellar mass functions are also briefly introduced.
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