  The gas in the cores of many clusters and groups of galaxies has a short
radiative cooling time. Energy from the central black hole is observed to flow
into this gas by means of jets, bubbles and sound waves. Cooling is thus offset
by heating. We discuss the mechanisms involved and observed in the X-ray
brightest clusters and explore the closeness of the heating/cooling balance. It
is surprisingly tight on the cooling side when soft X-ray spectra are examined.
Non-radiative cooling by mixing is suggested as a means to relax the apparent
strong lack of cooling. Nevertheless the heating and cooling must balance on
average to better than 20 per cent.
