Abstract: We give a brief overview of naked singularities, how these can form from gravitational collapse and their possible relevance in astrophysics. We investigate how the black hole formation process described by the Oppenheimer-Snyder scenario is affected once small pressures are introduced in the collapsing matter cloud. We show that the presence of pressures and inhomogeneities, however small, can change drastically the structure of the apparent horizon and the final fate of collapse.