Item response theory (IRT) models, in their many forms, are undoubtedly the most widely used models in large-scale operational assessment programs. They have grown from negligible usage prior to the 1980s to almost universal usage in largescale assessment programs, not only in the United States, but in many other countries with active and up-to-date programs of research in the area of psychometrics and educational measurement.Perhaps the most important feature leading to the dominance of IRT in operational programs is the characteristic of estimating individual item locations (difficulties) and test-taker locations (abilities) separately, but on the same scale, a feature not possible with classical measurement models. This estimation allows for tailoring tests through judicious item selection to achieve precise measurement for individual test takers (e.g., in computerized adaptive testing, CAT) or for defining important cut points on an assessment scale. It also provides mechanisms for placing different test forms on the same scale (linking and equating). Another important characteristic of IRT models is local independence: for a given location of test takers on the scale, the probability of success on any item is independent of that of every other item on that scale. This characteristic is the basis of the likelihood function used to estimate test takers' locations on the scale.Few would doubt that ETS researchers have contributed more to the general topic of IRT than individuals from any other institution. In this chapter we briefly review most of those contributions, dividing them into sections by decades of publication. Of course, many individuals in the field have changed positions between