Recently, the $\Lambda$ polarization has been observed at relativistic heavy-ion collider (RHIC) and large hadron collider (LHC). This observation has inspired many studies on spin dynamics of quantum chromodynamics (QCD) many-body physics, thus opening a new avenue to studying the hot and dense nuclear matter.This paper reviews the recent progress of spin effects in relativistic heavy-ion collisions, with an emphasis on the quantum correlation between spin and motion in QCD matter, including newly discovered shear-induced polarization (SIP), a novel effect that fluid shear polarizes the spin. The linear response theory’s applications to studying those effects are also systematically reviewed. Finally, their observational signatures in experiments are discussed.