The double-pulsar system J0737-3039 is one of the most promising
discovery in the astrophysics of the neutron stars.  
Its orbital parameters enable unique tests of the theories of Gravity 
and make the system a unprecedented laboratory for the physics of highly 
condensed matter. 
The high orbital inclination favors the possibility of using the radio 
beams from the two sources as a probe for investigating the so far 
unaccessible magnetosphere of a pulsar. The discovery of this system also 
increases of about a order of magnitude the estimate of the merger rate 
of double neutron stars systems, opening new opportunities for the 
current generation of gravitational wave detectors. The status of the 
multiwavelength observations performed in the 22 months since the 
discovery is presented and short and long term perspectives are discussed.