The binary Rasch model is one of the cornerstones of modern item response theory and has been extended to a whole family of models. It has been designed as a probabilistic measurement model that clearly separates person and item parameters allowing to infer on item parameters without reference to person parameters. The Rasch model and the competing normal-ogive model were the first latent trait models that have been formulated in a clear-cut way. In this chapter, the Rasch model is considered, alternative binary models will be considered separately in the following chapter.