  Deep field observations are an essential tool to probe the cosmological
evolution of galaxies. In this context, X-ray deep fields provide information
about some of the most energetic cosmological objects: active galactic nuclei
(AGN). Astronomers are interested in detecting sufficient numbers of AGN to
probe the accretion history at high redshift. This talk gives an overview of
the knowledge resulting from a highly complete soft X-ray selected sample
collected with ROSAT, XMM-Newton and Chandra deep fields. The principal outcome
based on X-ray luminosity functions and space density evolution studies is that
low-luminosity AGN evolve in a dramatically different way from high-luminosity
AGN: The most luminous quasars perform at significantly earlier cosmic times
and are most numerous in a unit volume at cosmological redshift z~2. In
contrast, low-luminosity AGN evolve later and their space density peaks at
z~0.7. This finding is also interpreted as an anti-hierarchical growth of
supermassive black holes in the Universe. Comparing this with star formation
rate history studies one concludes that supermassive black holes enter the
cosmic stage before the bulk of the first stars. Therefore, first solutions of
the so-called hen-egg problem are suggested. Finally, status developments and
expectations of ongoing and future extended observations such as the XMM-COSMOS
project are highlighted.
