Gravitational collapse of matter clouds is a fundamental process in astrophysics, cosmology, and black hole physics today. After giving a basic introduction and review on recent interesting developments here, the purpose of this talk is to raise the possibility whether a probabilistic or stochastic treatment of collapse could create interesting new insights in this arena. In this context, specific classes of important collapse models, such as the Vaidya radiation collapse, Lemaitre-Tolman-Bondi dust collapse, and others will be discussed in some detail to point out the criticality and phases of black hole and naked singularity formation as collapse endstates.
