Singularities are regions of space where the density of matter, or the curvature of spacetime, becomes infinite. In such locales, the standard concepts of space and time cease to have any meaning.
Singularities are predicted to occur in all black holes and also in certain models of the Universe. For example, open Friedmann models of the Universe possess a singularity in the finite past, while the closed models have both an initial and final singularity. In general, cosmic censorship hides singularities behind event horizons, the exception being the initial singularity of the Big Bang.