  AGN feedback stands for the dramatic impact that a SMBH can make on its
environment. It has become an essential element of models that describe the
formation and evolution of baryons in massive virialized halos. The baryons'
radiative losses in the cores of these halos might lead to massive cooling and
vigorous star formation on the order of 10-1000 Msun/yr, whereas observations
show that the star formation rates are considerably less. It has now become
clear from an observational, theoretical and simulation perspective that the
activity of the central SMBH compensates for gas cooling losses and prevents
very high star formation rates in massive galaxies, which otherwise would be
much brighter than observed today. While AGN feedback is important over a broad
range of halo masses, the most massive objects like galaxy groups and clusters
truly provide outstanding laboratories for understanding the intrinsic details
of AGN feedback. Partly, this is because in the nearby massive objects we can
directly see what AGN feedback is doing to its surrounding hot halo in
exquisite details, as opposed to less massive systems. Yet another reason is
that in the most massive objects, the magnitude of AGN feedback has to be
extremely large, providing the most stringent constraints. In a nutshell, the
AGN feedback paradigm in groups and clusters postulates that (i) a SMBH in the
center of a halo can release a vast amount of energy, (ii) this energy can be
intercepted and thermalized by the gaseous atmosphere and (iii) the system
self-regulates so that the energy released scales with the properties of the
halo. A combination of multi-wavelength observations provides compelling
evidence of the AGN feedback importance. Similarly, theoretical arguments
suggest that self-regulation might be a natural property of a system consisting
of a gaseous atmosphere and a SMBH at the bottom of the potential well.
