We constrain the number density and evolution of Compton-thick (CT) Active Galactic Nuclei (AGN). 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 a combination of X-ray and mid-IR parameters. To find CT AGN at high redshifts we study the properties of a sample of 211 objects in the Extended Chandra Deep Field-South selected based on their very high mid-IR to optical flux ratios. We present significant evidence supporting the CT AGN nature of a large fraction of these sources, including a strong stacked X-ray signal. By performing spectral fitting to the rest-frame UV/optical light (dominated by the host galaxy) we found evidence for a significant young stellar population, indicating that these sources are experiencing considerable star-formation. Using this sample we measured the space density of CT AGN at z~2, finding a strong evolution in the number of high-luminosity sources from z=1.5 to 2.5. Such strong evolution was not predicted by any existing AGN luminosity function, but can be accurately explained by a simple prescription in which every new quasar is generated by a major merger of two gas-rich massive galaxies, which is originally heavily obscured and after ~100 Myrs removes most of the surrounding gas and dust to reveal an unobscured quasar.