Michael Kramer (MPIfR/JBCA) gave a captivating and eloquent talk this morning on using pulsars as tests for GR and as constraints on alternative theories of gravity. It's possible to use pulsar data to measure post-Keplerian parameters of the only known double pulsar system, and GR passes all the tests with flying colours. Measurements of other binary pulsar systems (PS + a white dwarf, for example) very probably put an end to MOND and other TeVeS gravity theories.Pulsar timing is precise to 10^-18 s, more precise than atomic clocks and it's apparently possible to notice irregularities in the terrestrial atomic timescale. Perihelion precession of pulsar binary systems is of order of degrees/year, meaning that Newtonian dynamics are completely inadequate here (one would be hopelessly lost soon, if she tried to navigate her spaceship in the system using Newton's dynamics. The stars would be out of place).
This image, showing the change in revolution time in binary pulsar system, came up. It's the strongest proof of gravitational wave existence so far, showing how the system radiates its energy away as ripples in the spacetime. The uncertainties are too small to picture.