Because of the prevalence of both nonnormal and categorical data in empirical research, this chapter focuses on issues surrounding the use of data with these characteristics. Specifically, we review the assumptions underlying NT estimators. We describe nonnormal and categorical data and review robustness studies of the most popular NT estimator, maximum likelihood (ML), in order to understand the consequences of violating these assumptions. Most importantly, we discuss three popular strategies often used to accommodate nonnormal and/or categorical data in SEM: 1. Weighted least squares (WLS) estimation, 2. Satorra-Bentler (S-B) scaled χ² and robust standard errors, and 3. Robust diagonally weighted least squares (DWLS) estimation. For each strategy, we present the following: (a) a description of the strategy, (b) a summary of research concerning the robustness of the χ²-statistic, other fit indices, parameter estimates, and standard errors, and (c) a description of implementation across three software programs.