  Penrose's crucial contributions to General Relativity, symbolized by his 1965
singularity theorem, received (half of) the 2020 Nobel prize in Physics. A
renewed interest in the ideas and implications behind that theorem, its later
developments, and other Penrose's ideas improving our understanding of the
gravitational field thereby emerged. In this paper I highlight some of the
advancements motivated by the theorem that were developed over the years. I
also identify some common misconceptions about the theorem's implications. A
modern perspective on the concept of closed trapped submanifolds, based on the
mean curvature vector, is advocated.
