We investigate the properties of relativistic charged fluid spheres in GR. Phenomenological equilibrium and stability properties are discussed. The linear eigenmode equation for radial perturbations is derived [1]. Charged spheres have been proposed as candidates to form naked singularities in GR and allow for configurations of higher compactness (x=2M/r) than their non-charged counterparts. We also show some results of our 1D code to evolve spherically symmetric barotropic, ideal fluids in GR. Our plan is to map out the potential barrier separating black holes from compact stars, paying special attention to non-linear mode coupling effects close to the maximum mass limit. Several scenarios can help to penetrate the barrier, like mass accretion or cooling. This continues the line of research of critical phenomena in gravitational collapse, applied to compact stars. [1] A. Brillante and I. N. Mishustin, EPL, 105 (2014) 39001