Chapter 1 lays out our motivation, puzzle, and research questions. Borders are one of the defining institutions of international relations. Borders establish the sovereign domain of the territorial state, within which actors have the right to govern, tax, conscript, and exploit resources. Stable borders facilitate bilateral trade, tourism, and threat reduction, the latter of which allows states to spend a larger percentage of finite resources on domestic infrastructure and social programs rather than defense. Some neighbors, however, experience failed settlement, producing some of the most violent and enduring conflict between states in modern international relations history. Despite the importance of borders, we know little about what causes failed delineation; nor have we adequately explored the consequences of that failure. Our book addresses this puzzle by answering three interconnected questions. What factors increase and decrease the likelihood of successful delineation of territorial borders, what effect does failed settlement have on rivalry formation, and how do rivals eventually settle their disputed borders and terminate these enduring competition?