[en] The 1974 discovery, by Russell A Hulse and Joseph H Taylor, of the first binary pulsar, PSR B1913+16, opened up new possibilities for the study of relativistic gravity. PSR B1913+16, as well as several other binary pulsars, provided direct observational proof that gravity propagates at the velocity of light and has a quadrupolar structure. Binary pulsars also provided accurate tests of the strong-field regime of relativistic gravity. General relativity has passed all of the binary pulsar tests with flying colors. The discovery of binary pulsars also had very important consequences for astrophysics, leading to accurate measurement of neutron star masses, improved understanding of the possible evolution scenarios for the co-evolution of binary stars, and proof of the existence of binary neutron stars emitting gravitational waves for hundreds of millions of years, before coalescing in catastrophic events radiating intense gravitational wave signals, and probably also leading to important emissions of electromagnetic radiation and neutrinos. This article reviews the history of the discovery of the first binary pulsar, and describes both its immediate impact and its longer-term effect on theoretical and experimental studies of relativistic gravity. (paper)