 The demand that singular structure be localized at a particular place bespeaks an old Aristotelian substantivalism that invokes the maxim, “To exist is to exist in space and time” (Earman 1995, p. 28). Aristotelian substantivalism here refers to the idea contained in Aristotle's contention that everything that exists is a substance and that all substances can be qualified by the Aristotelian categories, two of which are location in time and location in space. Such a criterion, however, may be inappropriate for features and properties of spacetime itself. Indeed, one need not consider anything so outré as incomplete, inextendible paths in order to produce examples of entities that seem undeniably to exist in some sense of the term or other, and yet which cannot have any even vaguely determined location in time and space predicated of them. Several essential features of a relativistic spacetime, singular or not, cannot be localized in the way that an Aristotelian substantivalist would demand. For example, the Euclidean (or non-Euclidean) nature of a space is not something with a precise location. (See Butterfield 2006 for discussion of these issues.) Likewise, various spacetime geometrical structures (such as the metric, the affine structure, the topology, etc.) cannot be localized in the way that the Aristotelian would demand, whether that demand be for localization at a point, localization in a precisely determinate region, or even just localization in a vaguely demarcated region. The existential status of such entities vis-à-vis more traditionally considered objects is an open and largely ignored issue (Curiel 1999, 2016; Butterfield 2006). Because of the way the issue of singular structure in relativistic spacetimes ramifies into almost every major open question in relativistic physics today, both physical and philosophical, it provides a peculiarly rich and attractive focus for these sorts of questions. 