The Heating of the Intra Cluster Medium

X–ray observations indicate that non–gravitational processes play a key role in determining the distribution of the diffuse, X-ray emitting gas in clusters of galaxies (ICM). The effect of non–gravitational processes is imprinted in the ICM as an entropy minimum. Preheating models assume that the entropy minimum is present in the cosmic baryons well before collapse. On the other hand, observations of baryons in Lyα clouds show only a modest extra heating, ruling out the presence of such an entropy plateau in the majority of low–density baryons at high z. The problem is avoided in the internal heating scenario, where the heating occurs only inside virialized structures. However, for internal heating the energy needed to build the entropy minimum is in excess of 1 keV per particle. It is not clear which kind of source can heat the baryons: SNae seem to be inefficient by a factor of 3 or more. This energy crisis must be solved by other sources (like AGNs), unless we are missing some key aspect of the heating mechanism. The main questions for the next years will be: when and where is the excess entropy produced, and by which mechanism?