Following a summary of the basic principles of pulsar timing, we present a review of recent results from timing observations of relativistic binary pulsars. In particular, we summarize the status of timing observations of the much celebrated original binary pulsarPSR&hthinsp;B1913+16,draw attention to the recent confirmation of strong evidence for geodetic precession in this system, review the recent measurement of multiple post-Keplerian binary parameters forPSR&hthinsp;B1534+12,and describe the Parkes Multibeam survey, a major survey of the Galactic Plane which promises to discover new relativistic binary pulsar systems. ©1999 American Institute of Physics.