The process by which students are selected to perform successfully in graduate schools has generated a literature that is reviewed here to determine what predictors and what criteria are used for graduate student selection and to evaluate the relative success of the predictors used. The bulk of the research involves correlation analysis. The article is organized into the following five segments: (1) the criterion problem: (2) kinds of predictors; (3) aptitude variables as predictors: (4) environmental variables as predictors; and (5) personality variables as predictors. The results of many prediction studies are integrated using tabular presentations. Implications of the findings for making graduate student selection decisions are discussed. (Author/KE)