  It is well known that the radiative cooling time of the hot X-ray emitting
gas in the cores of most clusters of galaxies is less than 10^10 yr. In many
clusters the gas temperature also drops towards the centre. If we draw a causal
connection between these two properties then we infer the presence of a cooling
flow onto the central galaxy. High spectral resolution XMM-Newton data and high
spatial resolution Chandra data, show however a lack of X-ray emitting gas
below about one third of the cluster virial temperature. The explanation is
that some form of heating balances cooling. The smoothness and similarity of
the cooling time profiles and the flatness of the required heating profiles all
indicate that we must seek a relatively gentle, quasi-continuous (on timescales
<10^8 yr), distributed heat source. The likely such source is the central black
hole and its powerful jets which create bubble-like cavities in the inner hot
gas. We briefly review the general heating and cooling statistics in an X-ray
bright sample of cluster before we discuss the detailed situation in the
Perseus cluster, the X-ray brightest cluster in the Sky.
