A detailed description of five latent structure models of achievement measurement is presented. The first project paper, by David L. McArthur, analyzes the history of mental testing to show how conventional item analysis procedures were developed, and how dissatisfaction with them has led to fragmentation. The range of distinct conceptual and methodological approaches to achievement testing that now exist are discussed. The second paper, by Kenneth A. Sirotnik, analyzes measurement in achievement as a central and continuing problem in mental testing, highlighting the differences between the modern alternatives. Five papers by David L. McArthur, Bruce Choppin, Ronald K. Hambleton, Rand R. Wilcox and Noreen Webb individually treat Student-Problem (S-P) chart analysis, the Rasch model in item analysis, a three-parameter logistic model, latent class models, and generalizability theory. An analysis of reading comprehension data by four of the contributors and Raymond Moy is presented. J. Ward Keesling presents a summary paper on the empirical work carried out so far in testing different models on common sets of data. (Author/PN)