We explore the X-ray diagnostics of cosmic star formation history and of the growth of supermassive black holes that have come out of recent deep-field X-ray studies. We summarize the status of our understanding of the X-ray evolution of galaxies. We discuss lessons learnt from number-count plots, as also the criteria for distinguishing between normal/straburst galaxies and AGNs in deep X-ray surveys. Finally, we discuss recent results on the accretion history in the AGN phases during which supermassive black holes grew, in particular the intriguing "anti-hierarchical" growth of black holes.