The quest of the X-ray background, detected by Giacconi and colleagues in 1962, is now largely resolved. The interpretation in terms of discrete emission from active galactic nuclei put forward by Setti and Woltjer in 1973 and 1985 is basically correct. Almost all of the background has been resolved below 2 keV, while around 10keV only 50% and above 10keV a very small fraction has been resolved. There is thus sufficient discovery space for future high-resolution imaging telescope missions with hard X-ray response. In particular a better determination of the background flux and spectral shape is required above 10 keV. Population synthesis models can in principle explain the shape and intensity of the X-ray background by a mixture of absorbed and unabsorbed AGN and, in particular including a correction for the Compton-thick objects undetectable at X-rays, are roughly consistent with the mass distribution of dormant black holes in the local galaxies. The detailed evolutionary behavior of the AGN population is still a matter of intense study. The AGN evolution seems to go hand in hand with the evolution of galaxies, but one of the big surprises was the finding of an "anti-hierarchical" growth of black holes: while massive black holes (QSOs) are formed very early in the universe, the lower-luminosity, smaller mass black holes are formed considerably later. A theoretical understanding of this phenomenon is still lacking.

In the future, X-ray surveys that are both wide and deep are necessary in order to provide enough volume for a better measurement of the space density function of the rare high-luminosity AGN at large red-shifts. Several new surveys towards this goal are already underway, e.g., the Chandra Multiwavelength Project (Champ) [79]), the Chandra Large Area Synoptic X-Ray Survey (CLASXS) [95], the Extended Chandra

Deep Field South (PI: W.N. Brandt), or the XMM-Newton COSMOS Field (PI: G. Hasinger), which together should enrich the sample of z > 4 objects by about an order of magnitude. Ultimately, a new X-ray survey mission, like ROSITA [68] and the Dark Universe Observatory [27], which aim to survey large solid angles on the sky to considerable depth, could provide a factor of 100 increase in the AGN sample size.

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