Modeling and understanding the quark-gluon plasma (QGP) formed in high-energy heavy-ion collisions requires some knowledge about the low-energy structure of the colliding nuclei. The success of the hydrodynamic model of the QGP enables us today to carefully scrutinize how such an input from low-energy nuclear physics affects the final outcome of heavy-ion collisions. Recently, experimental data from multiple collision systems has become available from the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider, and has permitted us to identify unambiguous signatures of the structural properties of nuclei in the experimental measurements.
I review the status of the manifestations of so-called nuclear deformations, reflecting collective spatial correlations of nucleons in the nuclear wave functions, at high-energy colliders. I show that the expectations of low-energy nuclear physics appear to be consistently fulfilled by the observations at high energy, bringing confidence to our understanding of the collision processes. Hence, I discuss the prospects for theoretical and experimental work aimed at exploiting the structure of nuclei to further improve our understanding of the QGP, with an emphasis on collisions of light and medium-mass ions to be performed over the next two decades at the CERN LHC, and their synergy with the results of effective theories for nuclei rooted in QCD.