This paper reviews the existing multidimensional item response theory (IRT) models and demonstrates how one of the models can be applied to estimation of abilities from a test measuring more than one dimension. The purposes of this paper were threefold. First, the fundamental concepts required when considering multidimensional models for the interaction of a person and a test item were defined. These concepts included the multidimensional latent space, the item difficulty function, and the item discrimination function. These definitions were conceived as multidimensional generalizations of similar concepts in unidimensional IRT models. Second, six existing multidimensional models were reviewed and, on the basis of their similarities, were classified into three general categories. The characteristics of these categories were described, and the general Rasch model was selected for further study on the basis of ease of parameter estimation. Third, estimation procedures for the parameters of the general Rasch model were described and applied to a set of simulation data that had been generated according to a two-dimensional special case of the model. The results indicated that a very close correspondence had been obtained between the estimated item parameters and those used to generate the simulation data. (PN)