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In the BH-galaxy co-evolution framework, most of the star-formation (SF) andthe black hole (BH) accretion is expected to take place in highly obscuredconditions. Thus, obscured AGN are difficult to identify in optical or X-raybands, but shine bright in the IR. Moreover, X-ray background (XRB) synthesismodels predict that a large fraction of the yet-unresolved XRB is due to themost obscured (Compton thick, CT) of these AGN. In this work, we investigatethe synergies between putative IR missions (using SPICA, proposed for ESA/M5but withdrawn in October 2020, and Origins Space Telescope, OST, as`templates') and the X-ray mission Athena, which should fly in early 2030s, indetecting and characterizing AGN, with a particular focus on the most obscuredones. Using an XRB synthesis model, we estimated the number of AGN and thenumber of those which will be detected in the X-rays. For each AGN weassociated an optical-to-FIR SED from observed AGN with both X-ray data and SEDdecomposition, and used these SEDs to check if the AGN will be detected bySPICA-like or OST at IR wavelengths. We expect that, with the deepest Athenaand SPICA-like (or OST) surveys, we will be able to detect in the IR more than$90\,\%$ of all the AGN (down to L$_{2-10\text{keV}} \sim 10^{42}\,$erg/s andup to $z \sim 10$) predicted by XRB synthesis modeling, and we will detect atleast half of them in the X-rays. Athena will be extremely powerful indetecting and discerning moderate- and high-luminosity AGN. We find that themost obscured and elusive CT-AGN will be exquisitely sampled by SPICA-likemission or OST and that Athena will allow a fine characterization of themost-luminous ones. This will provide a significant step forward in the processof placing stronger constraints on the yet-unresolved XRB and investigating theBH accretion rate evolution up to very high redshift ($z \ge 4$).

The role of SPICA-like missions and the Origins Space Telescope in the quest for heavily obscured AGN and synergies with Athena