The european X-ray observatory (EXOSAT), which was launched in 1983 and which finished operations in April 1986, has brought a rich harvest of results in the period 1984-1987, surveyed here. The EXOSAT payload consisted of three sets of instruments: two low energy imaging telescopes (LE:E<2 KeV), a medium-energy experiment (ME:E=l-50KeV) and a gas scintillation proportional counter (GSPC:E=2-20KeV). Over most of the energy range covered, EXOSAT was not more sensitive than its predecessor, the american EINSTEIN satellite. But the EINSTEIN satellite is far from having exhausted the treasures of the X-ray sky. And EXOSAT, thanks to its elliptical 90-hour orbit, had the extra advantage of being able to make long, continuous observations of interesting objects, lasting up to 72 hours. Thus, EXOSAT was very well suited for variability studies, and many of its most important findings are in this area. EXOSAT observations sample a vide range of astrophysical sources: X-ray binaries, cataclysmic variables and active stars; supernova remnants and the interstellar medium; active galactic nuclei, and clusters of galaxies. Among the highlights, let us mention: