In this talk, we investigate strong singularity formation in compressible fluids. We will consider the compressible three-dimensional Navier-Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data for which the corresponding solutions to both equations implode (with infinite density) at a later time at a point, and completely describe the associated formation of singularity. An essential step in the proof is the existence of smooth self-similar solutions to the compressible Euler equations for quantized values of the speed. All blow up dynamics are then obtained by perturbation, for the Navier-Stokes problem are of type II (non self-similar).