This book of edited contributions provides a wide-ranging survey of the use of probability models for ranking data and it introduces new methods for the statistical analysis of ranking data. The contributors are drawn from a variety of fields including psychology, sociology, and the health sciences as well as statistics. Consequently, many researchers whose work involves the study of ranked data will find much of practical interest here. The papers cover the following topics: basic models and mixture models; inference from full and partial rankings; amalgamation and consensus; and paired ranking and unfolding. A foreward by Persi Diaconis draws together some of the mathematical ideas underlying this subject and explores its links with the statistical analysis of permutations.