We review results from cosmic X-ray surveys of active galactic nuclei (AGNs) over the past ~ 15 yr that have dramatically improved our understanding of growing supermassive black holes in the distant universe. First, we discuss the utility of such surveys for AGN investigations and the capabilities of the missions making these surveys, emphasizing Chandra, XMM-Newton, and NuSTAR. Second, we briefly describe the main cosmic X-ray surveys, the essential roles of complementary multiwavelength data, and how AGNs are selected from these surveys. We then review key results from these surveys on the AGN population and its evolution ("demographics"), the physical processes operating in AGNs ("physics"), and the interactions between AGNs and their environments ("ecology"). We conclude by describing some significant unresolved questions and prospects for advancing the field.