The occurrence of third-party intervention is a hallmark of many of the most devastating conflicts in world history, because the entrance of third parties into a conflict expands the scope of the violence, amplifies the severity and duration of the fighting, and increases the overall amount of death and destruction. Even in international conflicts in which intervention does not occur, the possibility that third parties may intervene can affect the behavior of disputants and therefore shape the way disputes evolve and are eventually resolved. This dissertation develops a theory of intervention by laying out a story about how strategic third parties and disputants make interdependent decisions in the context of an ongoing militarized dispute, and then formalizing this story into a simple-game theoretic model. The theory produces a general, causal explanation for third-party intervention that specifies the precise conditions under which it does and does not occur. Overall, the theory predicts approximately two-thirds of cases correctly when subjected to rigorous empirical tests. In addition, the theory produces theoretically-interesting, empirically-supported insights about the relationships between the resources of the actors involved in a militarized dispute and the likelihood that intervention occurs. The dissertation concludes with an application of the theory to the debate in the international relations literature over whether balancing or bandwagoning is the more common form of intervention. The application shows that the theory produces a more powerful explanation for the occurrence of balancing and bandwagoning than the existing literature offers, and suggests that the debate is misspecified.