  We analyse very deep X-ray and mid-IR surveys in common areas of the Lockman
Hole and the HDF North to study the sources of the X-ray background (XRB) and
to test the standard obscured accretion paradigm. We detect with ISO a rich
population of X-ray luminous sources with red optical colours, including a
fraction identified with Extremely Red Objects (R-K > 5) and galaxies with SEDs
typical of normal massive ellipticals or spirals at z ~ 1. The high 0.5-10 keV
X-ray luminosities of these objects (1E43-1E45 erg/s) indicate that the
ultimate energy source is gravitational accretion, while the X-ray to IR flux
ratios and the X-ray spectral hardness show evidence of photoelectric
absorption at low X-ray energies. An important hint on the physics comes from
the mid-IR data at 6.7 and 15 um, well reproduced by model spectra of
completely obscured quasars under standard assumptions and l.o.s. optical
depths tau ~ 30-40. Other predictions of the standard XRB picture, like the
distributions of intrinsic bolometric luminosities and the relative fractions
of type-I and -II objects (1:3), are also consistent with our results. Obscured
gravitational accretion is then confirmed as being responsible for the bulk of
the X-ray background, since we detect in the IR the down-graded energy
photoelectrically absorbed in X-rays: 63% of the faint 5-10 keV XMM sources are
detected in the mid-IR by Fadda et al. (2001). However, although as much as 90%
of the X-ray energy production could be converted to IR photons, no more than
20% of the Cosmic IR Background can be attributed to X-ray loud AGNs.
