More than four decades ago, instrumental developments, such as those involving neutron activation and X-ray florescence, began to generate relatively large quantities of data from the analysis of archaeological materials. These data served as the basis for many models of long-distance exchange as a means of explaining the development of cultural complexity. I review aspects of this early history and the how use of compositional data is now more directed toward localized investigations of economic activity. Even with this refocus of research interest, studies involving material characterization appear to be declining. Using traditional citation, personal experience, and highly selective examples, I discuss the use of analytical techniques for studies of long-distance trade, as it developed and now confronts interpretive difficulties that are inherent in the data and rendered more so by use of abstract constructs and resource limitations.