This book consolidates knowledge on regression chain graph models, often referred to as regression graph models, with a particular emphasis on their parameterizations and inference for the analysis of categorical data. It presents regression graphs, their interpretation in terms of sequences of multivariate regressions, interpretable parameterizations for categorical data, and inference and model selection within the frequentist and Bayesian approaches. The aim is to reveal the benefits of this family of graphical models for statistical data analysis and to encourage applications of these models as well as further research in the field. Data and R code used in the book are available online. The text is primarily intended for graduate and PhD students in statistics and data science who are familiar with the basics of graphical Markov models and of categorical data analysis, and for motivated researchers in specific applied fields.