  Binary radio pulsar system J0737-3039 provides an exceptional opportunity to
study innermost structure of pulsar magnetospheres due to very tight orbit,
favorable directions of pulsars' rotation and magnetic axes and extremely
fortuitous orientation of the orbit. In this system the millisecond pulsar A is
eclipsed once per orbit. During eclipse a clear modulation at the 2.77 s period
of pulsar B is seen, pointing unambiguously to magnetospheric origin of
eclipses. A simple geometric model, based on the idea that the radio pulses are
attenuated by synchrotron absorption on the closed magnetic field lines of
pulsar B, can successfully reproduces the eclipse light curves down to
intricate details. This detailed agreement confirms the dipolar structure of
the neutron star's magnetic field.
  The model gives clear predictions for temporal evolution of eclipse profile
due to geodetic precession of pulsar B.
  In addition, pulsar B shows orbital modulations of intensity, being
especially bright at two short orbital phases. We showed that these modulations
are due to distortion of pulsar B magnetosphere by pulsar A wind which produces
orbital phase-dependent changes of the direction along which radio waves are
emitted. Thus, pulsar B is intrinsically bright at all times but its radiation
beam misses the Earth at most orbital phases.
