This article examines the role of spatial shape in the justification, practice, and study of territorial claims, focusing in particular on the concepts of contiguity and compactness. A territory is contiguous if all parts are connected to all other parts, and a territory is compact if all its parts are closely joined or densely packed spatially. Shaping territories to be contiguous and compact is often implicitly taken to be a worthwhile goal, in both empirical and normative assessments of territorial claims. This article focuses directly on these two concepts, taking a novel approach to the study of territory by raising questions about these foundational, but often unexamined, background assumptions. Interrogating territorial shape thus provides a useful means of examining arguments about the justice or legitimacy of the territorial rights attributed to states or peoples. The contingent origins of the concepts of contiguity and compactness suggest that evaluations of territorial shape have sometimes been based on an implicit affective ‘feel’ or emotional reaction as much as on logical or empirical argument. This conclusion allows us to rethink some of our unstated assumptions about the shapes of states and other political territories, and thus to reconsider the justice or legitimacy attributed to those claims.