  Extragalactic X-ray surveys are exceptionally powerful tools for studying the
evolution of supermassive black holes and their host galaxies, by detecting
large numbers of active galactic nuclei (AGN) and star-forming galaxies over a
wide range of redshifts and cosmic environments. With its sensitivity and
superb angular resolution, Chandra has been at the forefront of recent
extragalactic surveys. This article provides a brief overview of Chandra
surveys, and highlights a few recent results on the composition of the cosmic
X-ray background, insights on X-ray source populations, and links between AGN
and galaxy evolution, as well as discussing prospects for surveys with future
X-ray missions.
