Although we use X-rays for penetrating scans of the human body, the Earth’s atmosphere is almost completely opaque to X-rays, and X-ray astronomy has to be performed from outside the atmosphere. Observations started with rocket flights in the mid-XX century, and graduated to satellites in 1970 with the first orbiting X-ray observatory NASA’s Uhuru. Other countries with space agencies which have launched X-ray astronomy satellites since then include Japan. Germany, Italy, Russia, the United Kingdom, and also the European Space Agency ESA. X-ray telesopes need highly specialized focusing elements, using grazing incidence reflection which are illustrated here. The Sun’s corona, with temperatures of over a million degrees, has been a constant subject for X-ray astronomers, investigating solar activity and the solar wind. The highest temperature phase of the interstellar and intergalactic medium needs X-ray techniques for its study. Compact stars: notably neutron stars and stellar mass black holes, are studied via the X-ray emission from their atmospheres, and the nature of quasars as supermassive black holes at galaxy centres, rather than compact collections of massive stars, was first postulated due to their X-ray emission. X-ray astronomy gives us key information about the most energetic objects in the universe.