Relativistic heavy-ion collisions at RHIC and the LHC are aimed at studying the quark-gluon plasma and exploring QCD phase diagrams.Recently,it has been realized that these collisions also provide new opportunities to probe the structures of the colliding nuclei.By comparing theoretical calculations and experimental measurements,one can quantitatively constrain the structures of the ground state nuclei.In this paper,we review the progress in this new research area from both experimental and theoretical perspectives,including the study of the nuclear deformations,neutron skins,and α clusters for the colliding nuclei in 96Ru+96Ru,96Zr+96Zr,197Au+197Au,238U+238U,129Xe+129Xe,208Pb+208Pb,and 16O+16O collisions at RHIC and the LHC.