The Chandra Deep Fields (CDFs), being a major thrust among extragalactic X-ray surveys and complemented effectively by multiwavelength observations, have critically contributed to our dramatically improved characterization of the 0.5-8 keV cosmic X-ray background sources, the vast majority of which are distant active galactic nuclei (AGNs) and starburst and normal galaxies. In this review, I highlight some recent key observational results, mostly from the CDFs, on the AGN demography, the interactions between AGNs and their host galaxies, the evolution of non-active galaxy X-ray emission, and the census of X-ray galaxy groups and clusters through cosmic time, after providing the necessary background information. I then conclude by summarizing some significant open questions and discussing future prospects for moving forward.