Quasars at z>4 provide direct information on the first massive structures to form in the Universe. Recent ground-based optical surveys (e.g., the Sloan Digital Sky Survey) have discovered large numbers of high-redshift quasars, increasing the number of known quasars at z>4 to ~500. Most of these quasars are suitable for follow-up X-ray studies. Here we review X-ray studies of the highest redshift quasars, focusing on recent advances enabled largely by the capabilities of Chandra and XMM-Newton. Overall, analyses indicate that the X-ray emission and broad-band properties of high-redshift and local quasars are reasonably similar, once luminosity effects are taken into account. Thus, despite the strong changes in large-scale environment and quasar number density that have occurred from z~0-6, individual quasar X-ray emission regions appear to evolve relatively little.