Abstract: I will discuss the stability of nonrotating relativistic stars (white drawfs, neutron stars etc.) modeled by the Euler-Einstein equation. Upon specifying an equation of state, spherically symmetric steady states of the Einstein-Euler system are embedded in 1-parameter families of solutions, characterized by the value of their central redshift. In the 1960s, Zel'dovich and Wheeler et al. formulated a turning point principle which states that the spectral stability can be exchanged to instability and vice versa only at the extrema of mass along the mass-radius curve. Moreover, the bending orientation at the extrema determines whether a growing mode is gained or lost. We proved the turning point principle and provided a detailed description of the linearized dynamics. One of the corollaries of our result is that the number of growing modes grows to infinity as the central redshift increases to infinity. I will also discuss the critical phenomena for gravitational collapse and its relation to the dynamics near unstable stars. This is joint work with Hadzic.