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The Regression Discontinuity (RD) design is one of the most popular and credible research designs for program evaluation and causal inference. This volume 38 of Advances in Econometrics collects twelve innovative and thought-provoking contributions to the RD literature, covering a wide range of methodological and practical topics. Some chapters touch on foundational methodological issues such as identification, interpretation, implementation, falsification testing, estimation and inference, while others focus on more recent and related topics such as identification and interpretation in a discontinuity-in-density framework, empirical structural estimation, comparative RD methods, and extrapolation. These chapters not only give new insights for current methodological and empirical research, but also provide new bases and frameworks for future work in this area. This volume contributes to the rapidly expanding RD literature by bringing together theoretical and applied econometricians, statisticians, and social, behavioural and biomedical scientists, in the hope that these interactions will further spark innovative practical developments in this important and active research area.