Singularities are a generic feature in general relativity. The Penrose singularity theorem relates the presence of a black hole to the existence of a closed trapped surface. In this talk we will describe how such trapped surfaces can form during evolution from initial data that do not already contain trapped surfaces. We focus on the case of spherically symmetric solutions of the Einstein-Euler equations describing a compressible fluid commonly used to model stellar structures in astrophysics. The initial data constructed to observe such trapping phenomena are static solutions with certain admissible large localized perturbations. This is partly joint work with P. LeFloch and L. Andersson.