The first measurements of X-ray emission from space were made just over fifty years ago with the arrival of the space rocket era. The first X-ray detections of objects outside our Solar System was made during a historic sounding rocket flight experiment led by Riccardo Giacconi in 1962. Giacconi received the 2002 Nobel Prize for " for pioneering contributions to astrophysics, which have led to the discovery of cosmic X-ray sources" (Nobel prize physics 2002). The flight resulted in the detection of the cosmic X-ray background and an accreting neutron star binary Scorpius X-1.
The first detection of X-rays from a galaxy other than the Milky Way occurred during a sounding rocket flight similar to the 1962 Giacconi flight. The flight detected a satellite galaxy of the Milky Way, the Large Magellanic Cloud and was published in March of 1969 by Hans Mark and his collaborators. The study of X-ray emission from "normal" galaxies (those that do not have their X-ray emission clearly dominated by a supermassive black hole) began truly in earnest starting in 1978 using measurements from the space mission Einstein. These first systematic measurements were largely led by Dr. Pepi Fabbiano, widely regarded as the mother of the field of X-ray studies of galaxies (e.g., Fabbiano et al. 1982 ).
Later space missions like ROSAT, XMM-Newton, Chandra and now NuSTAR have improved our understanding of the physical origin of the X-ray emission from galaxies, and the story continues to this day.