Deep surveys of the cosmic X-ray background are reviewed in the context of observational progress enabled by the Chandra X-ray Observatory and the X-ray Multi-Mirror Mission-Newton. The sources found by deep surveys are described along with their redshift and luminosity distributions, and the effectiveness of such surveys at selecting active galactic nuclei (AGN) is assessed. Some key results from deep surveys are highlighted including (1) measurements of AGN evolution and the growth of supermassive black holes, (2) constraints on the demography and physics of high-redshift AGN, (3) the X-ray AGN content of infrared and submillimeter galaxies, and (4) X-ray emission from distant starburst and normal galaxies. We also describe some outstanding problems and future prospects for deep extragalactic X-ray surveys.
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