An overview of direct mass measurements of exotic nuclei at the FRS-ESR facility at GSI is given. The nuclides are produced at relativistic energies by projectile fragmentation and fission, separated in-flight at the fragment separator FRS and injected into the storage ring ESR. Mass measurements are performed using Schottky and Isochronous Mass Spectrometry, which both allow for high precision measurements with single-ion sensitivity. Recent experimental developments are summarized, and examples for measurement results are given, including applications in nuclear structure physics and astrophysics, comparisons with mass predictions, and the search for new isotopes and isomers. Further research potential will be available at next-generation fragment-separator-storage-ring facilities such as the Super-FRS-CR-NESR complex at the future FAIR facility.