Modeling circular distributions in a flexible and meaningful way has been the motivation for a prolific topic within circular statistics. Flexible distribution models aim to capture not only location or concentration features, but also peakedness and skewness, and one may consider nonparametric approaches (such as kernel method) for that purpose. However, if there is also an interest in interpreting the aforementioned characteristics, then flexible parametric models are the choice. In this Chapter, we will revise some circular parametric families (from two-parameter to four-parameter models), emphasizing their advantages and limitations, and checking their performance on a real case study on car accidents.