  Detection of the copious amount of X-ray emission from the dilute hot plasma
in galaxy clusters suggests that a substantial fraction of the central
intracluster medium (ICM) is cooling radiatively on a time scale much faster
than the Hubble time. Theoretical models predict the cooling rate as high as
about few hundred to few thousand solar mass per year, which would be then made
available for the formation of new stars in the core of these clusters.
However, systematic studies of the cores of such clusters failed to detect the
expected reservoirs of cooled gas. Thus, the gas in the cores of galaxy
clusters is losing substantial amount of energy in the form of X-rays but is
not cooling. This in turn point towards the famous cooling flow paradox and
hence demands some intermittent heating to balance the cooling over such a long
period. Several sources have been suggested to counteract on the cooling of the
ICM, however, the AGN feedback appeared to be the most promising and enough
energetic source to resist cooling of the ICM in the cores of such clusters. In
this presentation I will provide a brief overview on the feedback processes
that are involved in the cores of the galaxy clusters with an emphasis on the
AGN feedback and its observable signatures.
