Statistical models are useful devices for understanding the essential features of a set of data. Models, however, are nearly always approximate descriptions of more complicated processes. Because of this inexactness, the study of the variation in the results of an analysis under modest modifications of a problem formulation becomes important. Components of a problem that are critical for the interpretation of the results are called influential. This paper contains a review of selected topics in influence assessment with emphasis on recent developments. Topics covered include a discussion of general ideas behind influence diagnostics, a comparison of case deletion diagnostics in linear regression, and the unifying approach to influence developed by Cook (1986). © 1987, Carfax Publishing Company. All rights reserved.