This volume covers extensions of the Rasch model, one of the most researched and applied models in educational research and social science. The 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 volume collects research and development work on extensions of the Rasch model and is aimed at relaxing some fundamental constraints of the original model, more specifically, the item homogeneity assumption and the person homogeneity assumption.