| The diffuse X-ray background (XRB) is the superposition
              of the X-ray emission of individual Active Galactic Nuclei
              (AGN) across cosmic time. AGN population synthesis models
              (e.g. Akylas et al.
                2012) can reconstruct the shape and overall
              normalisation of the XRB spectrum by invoking a population
              of heavily obscured AGN. There are still uncertainties on
              the evolution of AGN, particularly heavily obscured ones,
              with direct impact on models for the composition of the
              XRB.  Work is currently in progress to provide tighter
              observational constraints on the space density of AGN as a
              function of accretion luminosity, redshift and level of
              obscuration, which can then feedback to XRB population
              synthesis models. Of particular interest are estimates of
              the space density of the most deeply shrouded (Compton
              thick) AGN, i.e. those that are embedded within cocoons of
              dust and gas clouds with equivalent hydrogen column
              density logNH>24 (cm-2).  X-ray surveys have been extensively used over the years
              to improve our knowledge on the most heavily obscured AGN.
              They are advantageous over selections at other wavelengths
              because they provide clean AGN samples, minimal
              contamination by non-AGN and also allow direct measure of
              the level of obscuration of the central source via X-ray
              spectroscopy. Work is currently underway to improve
              analysis methodology and expand the survey data used in
              luminosity function calculations.  |