  The cosmological evolution of supermassive black holes (SMBHs) seems to be
intimately linked to their host galaxies. Active galactic nuclei (AGN) can be
probed by deep X-ray surveys. We review results from large X-ray selected
samples including first results from the XMM-Newton COSMOS survey. A new
picture arises from the fact that high-luminosity AGN grow earlier than
low-luminosity AGN. In particular, the space density of low-luminosity AGN
exhibits a significant decline for redshifts above z=1. This
'anti--hierarchical' growth scenario of SMBHs can be explained by two modes of
accretion with different efficiency. The population of Compton-thick sources
plays a key role in our understanding of the BH growth history. Their space
density and redshift distribution is relevant to estimate the SMBH mass
function. A comparison with the relic SMBH mass distribution in the local
Universe constrains the average radiative efficiency and Eddington ratio of the
accretion. We discuss a new synthesis model of Compton-thin and Compton-thick
sources that is in concordance with deep X-ray observations and in particular
predicts the right level of contribution of the Compton-thick source population
observed in the Chandra Deep Field South observations as well as the first
INTEGRAL and Swift catalogues of AGN. Currently, one of the most important
problems is the evolution of obscuration with redshift.
