  ROSAT deep and shallow surveys have provided an almost complete inventory of
the constituents of the soft X-ray background which led to a population
synthesis model for the whole X-ray background with interesting cosmological
consequences. According to this model the X-ray background is the ``echo'' of
mass accretion onto supermassive black holes, integrated over cosmic time. A
new determination of the soft X-ray luminosity function of active galactic
nuclei (AGN) is inconsistent with pure luminosity evolution. The comoving
volume density of AGN at redshift 2-3 approaches that of local normal galaxies.
This indicates that many larger galaxies contain black holes and it is likely
that the bulk of the black holes was produced before most of the stars in the
universe. However, only X-ray surveys in the harder energy bands, where the
maximum of the energy density of the X-ray background resides, will provide the
acid test of this picture.
