This volume covers extensions of the Rasch model, one of the most researched and applied models in educational research and social science. This collection contains 22 chapters by some of the most recognized international experts in the field. They cover topics ranging from general model extensions to applications in fields as diverse as cognition, personality, organizational and sports psychology, and health sciences and education. The Rasch model is designed for categorical data, often collected as examinees' responses to multiple tasks such as cognitive items from psychological tests or from educational assessments. The Rasch model's elegant mathematical form is suitable for extensions that allow for greater flexibility in handling complex samples of examinees and collections of tasks from different domains. In these extensions, the Rasch model is enhanced by additional structural elements that either account for differences between diverse populations or for differences among observed variables. Research on extending well-known statistical tools like regression, mixture distribution, and hierarchical linear models has led to the adoption of Rasch model features to handle categorical observed variables. We maintain both perspectives in the volume and show how these merged modelsRasch models with a more complex item or population structureare derived either from the Rasch model or from a structural model, how they are estimated, and where they are applied.