The orbits of giant exoplanets encode key clues on the formation history of planetary systems. However, it is difficult to determine the orbits of imaged giant planets that have orbital periods between decades and millennia with only measurements spanning ~10 years. The recent breakthrough for long-baseline interferometry to directly detect gas giant exoplanets has enabled a revolutionary 20-100x improvement in the astrometry of directly imaged exoplanets. I will present a uniform orbital analysis of all 17 exoplanets and 19 brown dwarf companions observed by the VLTI/GRAVITY interferometer through the ExoGRAVITY team. I will show how the unprecedented precision of GRAVITY has enabled precise orbits for companions from 3 to 300 AU. I will highlight some new measurements that are only possible with 50-microarcsecond GRAVITY astrometry: measuring planet masses through perturbations on the visual orbits of other planets in the system and searching for binary planets and moons through astrometry. Finally, I will present our analysis of the population-level orbital distribution of giant planets between 3-300 AU and how it compares to other samples.