As we have shown in this review, X-ray studies of galaxies are now yielding copious information on the properties of their XRB populations. The classification and study of these different populations is providing a unique tool for understanding the origin and evolution of XRBs, and for relating these sources to the evolution of the stellar populations of the parent galaxies, both in the nearby and the far-away universe.
This work would not have happened without the vision of Riccardo Giacconi, who pushed forward the high resolution X-ray telescope concept, and the work of Leon Van Speybroeck, who designed the Chandra optics. We thank the colleagues that have provided figures and comments (Martin Elvis, Albert Kong, Ann Hornschemeier, Vicky Kalogera, Jon Miller, Doug Swartz, Andreas Zezas, Harvey Tananbaum, Phil Kaaret, Jeff McClintock, Andrew King). This work benefitted by the Aspen Summer Workshop on Compact X-ray Sources (Summer 2002), and would not have been completed without the relentless prodding of Walter Lewin, to whom we are indebted. We aknowledge partial support from the Chandra X-ray Center under NASA contract NAS 8-39073.