More than fifty years have elapsed from the first discovery of gamma-ray bursts (GRBs) with American Vela satellites, and more than twenty-five years from the discovery with the BeppoSAX satellite of the first X-ray afterglow of a GRB. Thanks to the afterglow discovery and to the possibility given to the optical and radio astronomers to discover the GRB optical counterparts, the long-time mystery about the origin of these events has been solved. Now we know that GRBs are huge explosions, mainly ultra relativistic jets, in galaxies at cosmological distances. Starting from the first GRB detection with the Vela satellites, I will review the story of these discoveries, those obtained with BeppoSAX, the contribution to GRBs by other satellites and ground experiments, among them being Venera, Compton Gamma Ray Observatory, HETE-2, Swift, Fermi, AGILE, MAGIC, H.E.S.S., which were, and some of them are still, very important for the study of GRB properties. Then, I will review the main results obtained thus far and the still open problems and prospects of GRB astronomy.