Ordinal variables are widely used in psychological research, especially in the form of Likert items. Such data are still almost exclusively analysed with statistical models that falsely assume the ordinal variables to be metric. This practice can lead to problems such as distorted effect size estimates and inflated error rates. Therefore, we argue for the application of more appropriate ordinal models that make reasonable assumptions about the ordinal variables under study. From both theoretical and applied perspectives, we explain the ideas behind three major ordinal model classes; the cumulative, sequential and adjacent category models. We then use data sets on stem cell opinions, confidence ratings, and marriage time courses to show how to fit ordinal models in a fully Bayesian framework with the R package brms. Ordinal models provide better theoretical interpretation and numerical inference from ordinal data, and we recommend their widespread adoption. To this end, we provide guidelines for the application of ordinal models in psychological research.