This chapter introduces probabilistic models for supervised learning tasks where the prediction target is categorical. In binary classification, the target takes two values; models output the conditional probability of one of these, given the predictors. Logistic regression expresses the log odds as a linear function of the predictors and is fitted by minimising (regularised) cross-entropy loss. Minimising unregularised cross-entropy is equivalent to maximising likelihood, but in linearly separable cases, a maximum likelihood solution may not exist. Regularisation ensures the problem is well posed and helps control overfitting. In multiclass classification, the target can take K > 2 values, and models output a K-dimensional probability vector. Multinomial logistic regression expresses a K-dimensional score vector as a linear function of the predictors and applies the softmax function to convert scores into probabilities. k-nearest neighbours (k-NN) is a non-parametric method that estimates class probabilities from nearby training points. In high-dimensional predictor spaces, parametric models like logistic regression often outperform non-parametric ones like k-NN.