Item response theory (IRT) is the latent variable modeling approach widely used with educational and psychological test data. The determination of the dimensionality of the underlying latent trait (interpreted as examinee ability) is one of the fundamental questions in IRT. It is an important issue because of both substantive psycholological issues and for issues of statistical robustness in commonly used statistical procedures. One method of examining the the latent dimensionality is through the estimation of the covariances of item response pairs as conditioned on the unidimensional latent trait best measured by the exam. I will begin my talk by providing an introduction to IRT and the use of conditional covariances to investigate latent dimensionality. This will be followed by an overview of some of my current and ongoing research in the area, as well as some future research questions. The topics presented are: a rescaling of the conditional covariances to lessen their dependency on the item difficulties; the use of kernel smoothing and Monte Carlo methods to remove bias in latent dimensionality hypothesis test statistics based on the conditional covariance; and a new multidimensional IRT model based on the conditional covariance approach to multidimensionality.