A review of empirical likelihood

Empirical likelihood is a popular nonparametric analog of the usual parametric likelihood, inheriting many of the large-sample properties of the latter construct. This article presents a review of the empirical likelihood approach from its introduction 30 years ago, up to recent theoretical developments. Aspects of computation and connections between empirical likelihood and other likelihood-type quantities are also explored. The article ends with a discussion of some directions for future research.