This workshop focuses on gravitational singularities and the cosmic censorship conjectures, two intimately connected open problems in modern General Relativity. The event will explore recent research on weak and strong cosmic censorship, their relations to singularities arising in cosmological models or inside black holes, and how matter models affect the dynamics of these phenomena. This event will provide a platform for mathematicians and numerical physicists to discuss new developments and unanswered questions in the field.