This paper provides an up-to-date review of the relationship between item response theory (IRT) and (nonlinear) common factor theory and draws out of this relationship some implications for current and future research in IRT. Nonlinear common factor analysis yields a natural embodiment of the weak principle of local independence in appropriate loss functions that can be used to fit item response models and to assess their adequacy as descriptions of the data. The recognition of latent traits as synonymous with common factors gives appropriate guidance for interpretation in both unidimensional and multidimensional versions. Fixed-regressors theory based on the McDonald's (1979) treatment of common factor analysis was viewed, in principle, as applicable to any prescribed unidimensional model in item response theory, though so far it has been applied only to the rather inappropriate polynomial model. The advantages of this approach appear to be that it is not limited to the use of a linear combination rule for multiple latent traits and that it easily permits the introduction of interaction terms. Applications of the fixed-regressors treatment are subject to limitations of sample size, which may prove severe in the case of binary data, where large sample sizes are generally desirable. (PN)