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A gravitational singularity (sometimes spacetime singularity) is, approximately, a place where quantities which are used to measure the gravitational field become infinite. Such quantities include the curvature of spacetime or the density of matter. More accurately, a spacetime with a singularity contains geodesics which cannot be completed in a smooth manner. The limit of such a geodesic is the singularity.

The two most important types of spacetime singularities are curvature singularities and conical singularities. Singularities can also be divided according to whether they are covered by an event horizon or not (naked singularities). According to general relativity the initial state of the universe, at the beginning of the Big Bang, was a singularity, or single point. Another type of singularity predicted by general relativity is inside a black hole: any star collapsing beyond a certain point would form a black hole, inside which a singularity (covered by an event horizon) would be formed, as all the matter would flow into a certain point (or a circular line, if the black hole is rotating). These singularities are curvature singularities.