This book introduces basic and advanced concepts of categorical regression with a focus on the structuring constituents of regression. As reference for statisticians, applied researchers, and students it includes many topics not normally included in books on categorical data analysis. In addition to standard methods such as logit and probit models and their extensions to multivariate settings, the book presents more recent developments in regularized regression with a focus on the selection of predictors; tools for flexible nonparametric regression that yield fits that are closer to the data; non-standard tree-based ensemble methods; and tools for the handling of both nominal and ordered categorical predictors. Issues of prediction are explicitly considered in a chapter that introduces standard and newer classification techniques.