Professor Steven Hoffman discusses legal mechanisms available for coordinating international responses to transnational problems, their prospects, and their challenges. Global legal epidemiology is the scientific study of international law as a factor in the cause, distribution, and promotion of outcomes around the world. It involves evaluating the effectiveness of international legal mechanisms on the basis of their quantifiable effects and drawing implications for the development of future treaties. Prof Hoffman draws on examples from public health, including tobacco control and antimicrobial resistance, identifying wider lessons for potential international treaties in other domains such as the environment, human rights and trade.