This paper from the Journal of Economic Literature outlines the main principles and uses of Regression Discontinuity (RD) designs in research.
'It presents the basic theory behind the research design, details when RD is likely to be valid or invalid given economic incentives, explains why it is considered a “quasi-experimental” design, and summarizes different ways (with their advantages and disadvantages) of estimating RD designs and the limitations of interpreting these estimates. Concepts are discussed using examples drawn from the growing body of empirical research using RD.' (Lee & Lemieux, 2010)
Lee, D. S., & Lemieux, T. (2010). Regression discontinuity designs in economics. Journal of Economic Literature, 48, 281–355. Retrieved from http://gatton.uky.edu/Faculty/Ziliak/Lee_Lemieux_JEL2010.pdf