Abstract A brief account is given of the methodology and theory for the bootstrap. Methodology is developed in the context of the “equation” approach, which allows attention to be focussed on specific criteria for excellence, such as coverage error of a confidence interval or expected value of a bias-corrected estimator. This approach utilizes a definition of the bootstrap in which the key component is replacing a true distribution function by its empirical estimator. Our theory is Edgeworth expansion based, and is aimed specifically at elucidating properties of different methods for constructing bootstrap confidence intervals in a variety of settings. The reader interested in more detail than can be provided here is referred to the recent monograph of Hall (1992).