Scholars have long been fascinated by the role of international courts in the enforcement of international rule of law. They start with a foundational question: Can international courts affect how international law is implemented? In this review, we lay out four of the most common theoretical arguments for why international courts matter. We then interrogate these accounts. In particular, we examine their views on how much influence courts have and what the likely welfare consequences are for the signatories of an agreement. In so doing, we identify critical conditions that must obtain for court influence under each of the arguments. We then bring more recent scholarship to bear on the plausibility of these conditions. In particular, we examine what research on the structure of law, the preferences of judges, and institutional design implies about the efficacy of international courts based on the four foundational arguments. We conclude with suggestions for future research.


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