Gravitational microlensing was proposed thirty years ago as a promising method to probe the existence and properties of compact objects in the Galaxy and its surroundings. The particularity and strength of the technique is based on the fact that the detection does not rely on the detection of the photon emission of the object itself, but on the way its mass affects the path of light of a background, almost aligned source. Detections thus include not only bright, but also dark objects. Today, the many successes of gravitational microlensing have largely exceeded the original promises. Microlensing contributed important results and breakthroughs in several astrophysical fields as it was used as a powerful tool to probe the Galactic structure (proper motions, extinction maps), to search for dark and compact massive objects in the halo and disk of the Milky Way, to probe the atmospheres of bulge red giant stars, to search for low-mass stars and brown dwarfs and to hunt for extrasolar planets. As an extrasolar planet detection method, microlensing nowadays stands in the top five of the successful observational techniques. Compared to other (complementary) detection methods, microlensing provides unique information on the population of exoplanets, because it allows the detection of very low-mass planets (down to the mass of the Earth) at large orbital distances from their star (0.5 to 10 AU). It is also the only technique that allows the discovery of planets at distances from Earth greater than a few kiloparsecs, up to the bulge of the Galaxy. Microlensing discoveries include the first ever detection of a cool super-Earth around an M-dwarf star, the detection of several cool Neptunes, Jupiters and super-Jupiters, as well as multi-planetary systems and brown dwarfs. So far, the least massive planet detected by microlensing has only three times the mass of the Earth and orbits a very low mass star at the edge of the brown dwarf regime. Several free-floating planetary-mass objects, including free-floating planets of about Jupiter's mass, were also detected trough microlensing. Detections and non-detections inform us on the abundance of planets as a function of planetary mass and orbital distance. Recent microlensing studies imply that low-mass planets, in particular super-Earths, are far more abundant than giant planets, and reveal that there are, on average, one or more bound planets per Milky Way star. Future microlensing surveys will dramatically increase the number of microlensing alerts, thus providing unprecedented constraints on the planetary mass function, down to the mass of the Earth.