  The deep X-ray surveys performed by the two major X-ray observatories on
flight, Chandra and XMM, are being resolving the bulk of the cosmic X-ray
background (XRB) in the 2-10 keV energy band, where the sky flux is dominated
by extragalactic emission. Although the actual fraction depends on the absolute
sky flux, which is measured with an uncertainty of ~40%, most of the XRB is
already resolved. Optical identifications of the X-ray sources in the deep
surveys are being showing that these are mainly AGN, most of which being
obscured as predicted by population synthesis models. However, first results
indicate that the redshift distribution of the sources making the XRB seems to
peak at much lower redshift than predicted by the models. In this article I
will briefly review and discuss the measurements of the XRB spectrum and the
AGN synthesis models of the XRB. Then, I will introduce the Chandra and XMM
deep X-ray surveys, mainly focusing on the Chandra Deep Field North and South.
Finally, the properties of the X-ray sources populating the deep surveys will
be described and compared with the predictions of the most recent synthesis
models.
