We discuss the dynamics of polytropic gaseous stars described by the compressible Euler-Poisson system. For the static equilibria and for nontrivially accelerated fluids, the so-called physical vacuum naturally arises and we are led to study the vacuum free boundary value problems. We give a brief overview of the existence and stability theory, and we present a recent joint work with Mahir Hadzic on the nonlinear stability of self-similar expanding solutions in the mass-critical regime.