\noindent In this talk, I will discuss a novel class of nonlinear dispersive equations, which describe the dynamical evolution of self-gravitating relativistic matter. In fact, the analysis of these model equations will give a mathematical vindication of Chandrasekhar's acclaimed physical theory of gravitational collapse. In particular, I will present results concerning the well-posedness of the initial-value problem, the singularity formation of solutions (blowup), as well as solitary wave solutions and their stability. Time permitting, I will also discuss some recent and ongoing work. \\ \noindent This is partly joint work with J\"urg Fr\""ohlich (ETH Z\""urich)