In 1941, Horst noticed that a variable can be totally uncorrelated with the criterion and still improve prediction by virtue of being correlated with other predictors. He christened such variables suppressors, a title that implies that such variables suppress criterion-irrelevant variance in other predictors. During the 50 years that have passed since Horst's original analysis, the concept of suppression has been extended and reanalyzed. What follows provides a general approach to the analysis of suppression situations. This approach is based on coupling the analysis of 3 variate suppression situations with the applications of the concept of suppressor to the general linear model. The implications of the analysis are discussed, and some applications of the concept of suppression are provided.