AGN feedback from supermassive black holes (SMBHs) at the center of early type galaxies is commonly invoked as the explanation for the quenching of star formation in these systems. The situation is complicated by the significant amount of mass injected in the galaxy by the evolving stellar population over cosmological times. In absence of feedback, this mass would lead to unobserved galactic cooling flows, and to SMBHs two orders of magnitude more massive than observed. By using high-resolution 2D hydrodynamical simulations with radiative transport and star formation in state-of-the-art galaxy models, we show how the intermittent AGN feedback is highly structured on spatial and temporal scales, and how its effects are not only negative (shutting down the recurrent cooling episodes of the ISM), but also positive, inducing star formation in the inner regions of the host galaxy.

During the past decade observations across the electromagnetic spectrum have led to broad progress in the understanding of galaxy clusters and their far more abundant smaller siblings, groups. From the X-rays, where Chandra and XMM have illuminated old phenomena such as cooling cores and discovered new ones such as shocks, cold fronts, bubbles and cavities, through rich collections of optical data (including vast and growing arrays of redshifts), to the imaging of AGN outbursts of various ages through radio observations, our access to cluster and group measurements has leaped forward, while parallel advances in theory and modeling have kept pace.

This Special Session offered a survey of progress to this point, an assessment of outstanding problems, and a multiwavelength overview of the uses of the next generation of observatories. Holding the symposium in conjuction with the XXVIIIth General Assembly provided the significant advantage of involving not only a specialist audience, but also interacting with a broad cross-section of the world astronomical community.

We present long-term numerical simulations of powerful extragalactic relativistic jets in two dimensions. The jets are injected in a realistic atmosphere with powers 1044, 1045 and 1046 erg/s, during tens of Myrs. After this time, the jet injection is switched off. We follow the evolution of the jets and associated shocks from 1 kpc to hundreds of kiloparsecs during more than 100 Myrs. The 1045 erg/s jet was simulated with leptonic and baryonic composition. Our results show that, for powerful jets, the main heating mechanisms are the driving shock-wave and mixing. We discuss the implications that these results have in the frame of cooling flows in clusters.