One of the often-stated goals of principal component analysis is to reduce into a low-dimensional space most of the essential information contained in a high-dimensional space. According to several reasonable criteria, principal components do this optimally. From a practical point of view, however, principal components suffer from the disadvantage that each component is a linear combination of all of the original variables. Thus interpretation of the results and possible subsequent data collection and analysis still involve all of the variables. An alternative approach is to select a subset of variables that contain, in some sense, as much information as possible. Methods for selecting such “principal variables” are presented and illustrated with examples.