This paper reviews recent work in factor analysis of categorical variables. Emphasis is on the generalized least squares solution. A section on maximum likelihood solution focuses on extensions of the classical model, especially the normal case. Many of the recent developments have taken place within this context, and it provides a unified framework of exposition against which other models may be introduced in contrast. Section 2 provides a brief review of factor analysis of measured variables, setting up notation and formulas in this more familiar context. Section 3 introduces the common factor model for dichotomous items. Sections 4 and 5 discuss estimation of factor loadings from matrices of tetrachoric correlations, unweighted and weighted respectively. Section 6 discusses a full information solution based on the method of maximum likelihood. Finally, section 7 outlines a number of extensions to the basic model under investigation. These include Bayesian prior distributions on unique variances, confirmatory factor analysis, comparisons of factor structures between groups, and relaxation of assumptions about response functions and population distributions. Eight pages of references are included. (PN)