I will review a series of recent works on the construction of imploding singularities for self-gravitating fluids, describing stars. We will briefly explain a rigorous construction of the so-called Larson-Penston (LP) collapse - a Newtonian self-similarly imploding star solution discovered numerically in 1960s. We will then show the existence of its GR analogue, called the relativistic Larson-Penston (RLP) solution, which is a radially symmetric solution of the Einstein-Euler system. We will show that the RLP spacetime can be suitably flattened to obtain examples of spacetimes that dynamically form naked singularities from smooth initial data. This is based on several joint works with Yan Guo, Juhi Jang, and Matthew Schrecker.