Theory and methodology for exploratory factor analysis have been well developed for continuous variables. In practice, observed or measured variables are often ordinal. However, ordinality is most often ignored and numbers such as 1, 2, 3, 4, representing ordered categories, are treated as numbers having metric properties, a procedure which is incorrect in several ways. In this article we describe four approaches to factor analysis of ordinal variables which take proper account of ordinality and compare three of them with respect to parameter estimates and fit. The comparison is made both in terms of their relative methodological advantages and in terms of an empirical data example and two generated data examples. In particular, we discuss the issue of how to test the model and to measure model fit.