  The Regression Discontinuity (RD) design is one of the most widely used
non-experimental methods for causal inference and program evaluation. Over the
last two decades, statistical and econometric methods for RD analysis have
expanded and matured, and there is now a large number of methodological results
for RD identification, estimation, inference, and validation. We offer a
curated review of this methodological literature organized around the two most
popular frameworks for the analysis and interpretation of RD designs: the
continuity framework and the local randomization framework. For each framework,
we discuss three main topics: (i) designs and parameters, which focuses on
different types of RD settings and treatment effects of interest; (ii)
estimation and inference, which presents the most popular methods based on
local polynomial regression and analysis of experiments, as well as
refinements, extensions, and alternatives; and (iii) validation and
falsification, which summarizes an array of mostly empirical approaches to
support the validity of RD designs in practice.
