In astrophysical fluid dynamics, stars are considered as isolated fluid masses subject to self-gravity. A classical model to describe the dynamics of Newtonian stars is given by the gravitational Euler-Poisson system, which admits a wide range of star solutions that are in equilibrium or expand for all time or collapse in a finite time or rotate. In particular, using numerics, the Euler-Poisson system in the super-critical regime has been widely used inastrophysics literature todescribe the gravitational collapse, but its rigorous proof has been established only recently. The main challenge comes from thepressure, which actsagainstgravitational force. In this talk, I will discuss some recent progress on Newtonian dust-like collapse and self-similar collapse.