Unidimensional item response theory (IRT) models have become important tools to evaluate the quality of psychological and educational measurement instruments. Strictly unidimensional data are unlikely to be observed in practice because data often originate from complex multifaceted psychological traits. Still, unidimensional models may pro- vide a reasonable description of these data in many cases. In large-scale educational test- ing IRT is now the standard. Also for the construction and evaluation of psychological measurement instruments, IRT is starting to replace classical test theory (CTT). To illustrate this: When we recently obtained reviews of a paper from Psychological Assess- ment, one of the leading journals with respect to measurement and empirical evaluation of clinical instruments, it was stated that we did not have to explain in detail our IRT models because those models “are well-known to the audience of the journal.” We would not have received this message, say, 10 years ago. In this chapter, we distinguish parametric and nonparametric IRT models, and IRT models for dichotomous and polytomous item scores. We describe model assumptions, and we discuss model-data fit procedures and model choice. Standard unidimensional IRT models do not take test content into account, that is, IRT models are formulated without specific reference to maximum performance testing (intelligence, achievement) and typical performance testing (personality, mood, voca- tional interest). Yet, when these models are applied to different types of data, there are interesting differences that will be discussed in this chapter and that may guide the use of these models in different areas of psychology.