It is a heavy responsibility for me, as it would be for everybody else, to give a paper on the X-ray background (XRB) in this particular meeting, held in honor of Riccardo Giacconi. Everybody knows the enormous contribution that Riccardo has given to the development and better understanding of the subject from the very beginning 30 years ago up to now. A significant fraction of the results which I will describe in this paper either are his own results or are based on experiments which he conceived and led to success.
In Section 2 I will give a brief historical overview of the XRB problem, from its discovery up to the results obtained in the eighties with the HEAO-1 and EINSTEIN missions. During these years the origin of the XRB has been discussed mainly in terms of two alternative interpretations: the truly diffuse hypothesis (e.g. hot intergalactic gas) and the discrete source hypothesis. The existence of these radically alternative hypotheses has not been "neutral" with respect to devising experiments which wanted to study the XRB. In fact, if the XRB is mainly due to discrete sources, experiments aimed at studying the single sources responsible for it obviously need high angular resolution in order to study and resolve the large number of expected faint sources. Vice versa, if the XRB is mainly diffuse, source confusion is not a problem anymore and one could safely abandon the high angular resolution option. In this case the crucial experiment would be a measurement as accurate as possible of the spectrum in order to reveal the physical production processes. The two working hypotheses led various groups of scientists to design very different sets of experiments (Giacconi and Burg 1992). In Section 3 I will show some recent results from deep surveys with ROSAT. These surveys have already resolved into discrete sources ~ 60% of the measured XRB in the 1-2 keV band. The available optical identifications, still in progress, suggest that AGNs are the dominant population at these faint X-ray fluxes. Finally, in Section 4 I will discuss some recent results on the X-ray spectra of AGNs at higher energy and a few models which, making use of these data, are able to produce acceptable fits to the spectrum of the XRB up to about 100 keV.