Categorical time series are discretevalued time series having a qualitative range, which consists of a finite number of categories. As standard methods from realvalued time series analysis cannot be applied to such a kind of data, tailormade tools for the visualization of the time series, characterizing the marginal distribution and measuring serial dependence are presented. Also, common stochastic models for such time series are surveyed, including types of Markov models, discrete ARMA models, HiddenMarkov models, and regression models.