{Reference Type}: Journal Article {Title}: Nuclear structure opportunities with GeV radioactive beams at FAIR. {Author}: Aumann T;Bertulani CA;Duer M;Galatyuk T;Obertelli A;Panin V;Rodríguez-Sánchez JL;Roth R;Stroth J; {Journal}: Philos Trans A Math Phys Eng Sci {Volume}: 382 {Issue}: 2275 {Year}: 2024 Jul 23 {Factor}: 4.019 {DOI}: 10.1098/rsta.2023.0121 {Abstract}: The Facility for Antiproton and Ion Research (FAIR) is in its final construction stage next to the campus of the Gesellschaft für Schwerionenforschung Helmholtzzentrum for heavy-ion research in Darmstadt, Germany. Once it starts its operation, it will be the main nuclear physics research facility in many basic sciences and their applications in Europe for the coming decades. Owing to the ability of the new fragment separator, Super-FRagment Separator, to produce high-intensity radioactive ion beams in the energy range up to about 2 GeV/nucleon, these can be used in various nuclear reactions. This opens a unique opportunity for various nuclear structure studies across a range of fields and scales: from low-energy physics via the investigation of multi-neutron systems and halos to high-density nuclear matter and the equation of state, following heavy-ion collisions, fission and study of short-range correlations in nuclei and hypernuclei. The newly developed reactions with relativistic radioactive beams (R3B) set up at FAIR would be the most suitable and versatile for such studies. An overview of highlighted physics cases foreseen at R3B is given, along with possible future opportunities, at FAIR. This article is part of the theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'.