Weak cosmic censorship, trapped surfaces, and naked singularities for the Einstein vacuum equations

The weak cosmic censorship conjecture posits that, generically, all singularities in General Relativity arising from regular asymptotically flat initial data should have a complete future null infinity. While this conjecture remains wide open, it has inspired many mathematical works concerning topics such as trapped surface formation and the construction of naked singularities. In this article we will review some of these works and attempt to emphasize their interconnectedness.