Compton Thick (CT) AGN are a key ingredient of Cosmic X-ray Background (CXB) synthesis models, but are still an elusive component of the AGN population beyond the local Universe. Multi-wavelength surveys are the only way to find them at z > 0.1, and a deep X-ray coverage is crucial in order to clearly identify them among star forming galaxies. As an example, the deep and wide COSMOS survey allowed us to select a total of 34 CT sources. This number is computed from the 64 nominal CT candidates, each counted for its N H probability distribution function. For each of these sources, rich multi-wavelength information is available, and is used to confirm their obscured nature, by comparing the expected AGN luminosity from spectral energy distribution fitting, with the absorption-corrected X-ray luminosity. While Chandra is more efficient, for a given exposure, in detecting CT candidates in current surveys (by a factor ~2), deep XMM-Newton pointings of bright sources are vital to fully characterize their properties: NH distribution above 10^25 cm^-2, reflection intensity etc., all crucial parameters of CXB models. Since luminous CT AGN at high redshift are extremely rare, the future of CT studies at high redshift will have to rely on the large area surveys currently underway, such as XMM-XXL and Stripe82, and will then require dedicated follow-up with XMM-Newton, while waiting for the advent of the ESA mission Athena.
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