  In this article we review the measurements and understanding of the X-ray
background (XRB), discovered by Giacconi and collaborators 35 years ago. We
start from the early history and the debate whether the XRB is due to a single,
homogeneous physical process or to the summed emission of discrete sources,
which was finally settled by COBE and ROSAT. We then describe in detail the
progress from ROSAT deep surveys and optical identifications of the faint X-ray
source population. In particular we discuss the role of active galactic nuclei
(AGNs) as dominant contributors for the XRB, and argue that so far there is no
need to postulate a hypothesized new population of X-ray sources. The recent
advances in the understanding of X-ray spectra of AGN is reviewed and a
population synthesis model, based on the unified AGN schemes, is presented.
This model is so far the most promising to explain all observational
constraints. Future sensitive X-ray surveys in the harder X-ray band will be
able to unambiguously test this picture.
