Radio pulsars in double-neutron-star systems provide the best tests of
strong-field gravitational theories. I will present recent
observations of PSR B1534+12 and the double-pulsar system
J0737-3039A/B. In both cases, the pulsar timing observations are
sensitive to multiple relativistic corrections to the basic Keplerian
orbit, and therefore yield multiple tests of general relativity, with
the double pulsar providing the strongest test to date. I will also
discuss observations of geodetic precession and implications for the
formation of the two systems.