Categorical data consist of observations counted and subclassified into one among a set of disjoint, exhaustive groups. The groups may be defined on the basis of a single or a combination of qualitative characteristics and/or quantitative measurements. When such categorizations are to be modeled as probabilistic “responses” or “outcomes”, statistical analysis must be based upon discrete distributions and requires extensive generalization of the classical notions of regression and analysis of variance commonly used for continuous observations. This overview article reviews statistical inference for categorical data, from the basic issues in analyses of 2 × 2 contingency tables through generalized linear mixed models, with emphasis on approaches that have increasingly unified our concepts of categorical and continuous data modeling.