Title: Do we understand the cosmological evolution of AGN? Guenther Hasinger MPE, Garching Abstract: The majority of the X-ray background (XRB) below 10 keV has been resolved by ROSAT, Chandra and XMM-Newton deep surveys. However, a significant uncertainty still exists about the normalization of the XRB. I will show very recent results from the Swift BAT telescope, which basically confirm the low HEAO-1 normalization of the XRB, which in turn means that a higher fraction of the XRB is resolved. The luminosity function of X-ray selected AGN clearly shows a luminosity-dependent evolutiion, leading to an "anti-hierarchical" or "downsizing" behaviour, where the space density of luminous QSOs peak rather early (z>2) and that of lower luminosity Seyferts rather late (z<1) in the cosmic history. Assuming appropriate bolometric corrections, this evolution patterns holds for all wavelengths (hard X-ray, soft X-ray, optical, MIR) which are sampled well enough. An important ingredient into the bolometric correction is the fraction of obscured AGN with luminosity and redshift, and in particular the contribution of the elusive population of Compton-thick objects. I will show new results on these two questions. The "anti-hierarchical" evolution of AGN can only be understood in terms of two radically different modes of feeding the AGN. I will show that the violent merger conjecture probably only applies to the early luminous QSO evolution, while the general lower luminosity AGN must be fed through a slower, more gentle feeding mechanism. Recent results point to the direction that this AGN feeding mode may be connected to the "re-building" of disks around bulges containg pre-fabricated black holes. The bulk of modern AGN appear in the so called "green valley", which I interprete as objects coming back down from the red sequence through the slow accretion of fresh gas.