  After the first prediction to expect geodetic precession in binary pulsars in
1974, made immediately after the discovery of a pulsar with a companion, the
effects of relativistic spin precession have now been detected in all binary
systems where the magnitude of the precession rate is expected to be
sufficiently high. Moreover, the first quantitative test leads to the only
available constraints for spin-orbit coupling of a strongly self-gravitating
body for general relativity (GR) and alternative theories of gravity. The
current results are consistent with the predictions of GR, proving the
effacement principle of spinning bodies. Beyond tests of theories of gravity,
relativistic spin precession has also become a useful tool to perform beam
tomography of the pulsar emission beam, allowing to infer the unknown beam
structure, and to probe the physics of the core collapse of massive stars.
