The double pulsar system J0737-3039

J0737-3039 is the recently-discovered, first-known double-pulsar binary, a very compact double neutron star system in which both stars are observable as radio pulsars. In this review, we briefly describe the discovery and the studies which have been enabled by the unique properties of the system. These range from the most precise confirmation yet of the theory of general relativity, with the possibility of even more new tests and the measurement of second-order post-Newtonian effects, to studies of the magnetospheres and emission properties of the two pulsars. The discovery also results in a significant increase in the expected rate of occurrence of the mergers of double neutron star systems, and hence the likely rate of detection of such events by the new ground-based gravitational wave detectors.