 A spacetime singularity is a breakdown in spacetime, either in its geometry or in some other basic physical structure. It is a topic of ongoing physical and philosophical research to clarify both the nature and significance of such pathologies. When it is the fundamental geometry that breaks down, spacetime singularities are often viewed as an end, or “edge”, of spacetime itself. Numerous difficulties, however, arise when one tries to make this notion more precise. Breakdowns in other physical structures pose other problems, just as difficult. Our current theory of spacetime, general relativity, not only allows for singularities, but tells us that they are unavoidable in some real-world circumstances. Thus we apparently need to understand the ontology of singularities if we are to grasp the nature of space and time in the actual universe. The possibility of singularities also carries potentially important implications for the issues of physical determinism and the scope of physical laws. 