The purpose of this article is twofold. The first is to provide evaluative information on the recovery of model parameters and their standard errors for the two-parameter item response theory (IRT) model using different estimation methods by Mplus. The second is to provide easily accessible information for practitioners, instructors, and students about the relationships between IRT and item factor analysis (FA) parameterizations. Specifically, this is done using the "Theta" and "Delta" parameterizations in Mplus for unidimensional and multidimensional modeling with dichotomous and polytomous responses with and without the scaling constant D. The first objective aims at investigating differences that may occur when using different estimation methods in Mplus for binary response modeling. The second objective was motivated by practical interest observed among graduate students and applied researchers. The relations between IRT and Mplus FA "Theta" and "Delta" parameterizations are described using expressions without the use of matrices, which can be understood efficiently by applied researchers and students.