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 models—Rasch models with a more complex item or population structure—are derived either from the Rasch model or from a structural model, how they are estimated, and where they are applied. Matthias von Davier is a Senior Research Scientist in the Research & Development Division at Educational Testing Service. He is the author of WINMIRA, a software package for estimating latent class models, mixture distribution Rasch models, and hybrid Rasch models. The software grew out of his work with colleagues at the Methodology Department of the Institute for Science Education (IPN) in Kiel, Germany. Von Davier's current research is concerned with extensions of Rasch models and more general Item Response Theory (IRT) models to multidimensional, diagnostic models and with mixture distribution models, with statistical computation and estimation, and with applications of psychometric models in national and international educational assessments. Claus H. Carstensen is a junior Professor in the Psychometrics and Methodology Department at the IPN, Carstensen's work is concerned with multidimensional extensions of the Rasch model and applications of these models in intelligence and expertise research and educational assessments. He and Juergen Rost, head of the IPN's Methodology Department at the time, developed MULTIRA, a software package for multidimensional Rasch models. Before his current position, Carstensen was a Research Officer at the Australian Council of Educational Research where his focus was large-scale data analysis using multidimensional extensions of the Rasch model.