  We constrain the number density and evolution of Compton-thick Active
Galactic Nuclei (AGN), and their contribution to the extragalactic X-ray
background. In the local Universe we use the wide area surveys from the Swift
and INTEGRAL satellites, while for high redshifts we explore candidate
selections based on mid-IR parameters. We present the properties of a sample of
211 heavily-obscured AGN candidates in the Extended Chandra Deep Field-South
(ECDF-S) selecting objects with f24/fR>1000 and R-K>4.5. The X-ray to mid-IR
ratios for these sources are significantly larger than that of star-forming
galaxies and ~2 orders of magnitude smaller than for the general AGN
population, suggesting column densities of NH>5x10^24 cm^-2. The space density
of CT AGN at z~2 derived from these observations is ~10^-5 Mpc^{-3}, finding a
strong evolution in the number of LX>10^44 erg/s sources from z=1.5 to 2.5.
