  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.
