Collective dynamics of spin polarization in relativistic heavy-ion collisions

Recent heavy-ion collision experiments indicate that the matter produced in these events can develop significant spin polarization correlated with its vorticity. This observation has motivated extensions of conventional relativistic hydrodynamics to systems in which spin constitutes an additional dynamical degree of freedom. In this talk, I will outline the hydrodynamic formalism that has emerged from these developments and discuss the main lessons learned from its applications to heavy-ion phenomenology.