The significant increase of converter interfaced generation, consumption, storage, and transmission in power systems, results in the need to consider converter-driven stability in detail, as well as to study modelling and analysis methods with which such stability effects can be represented and investigated. Due to the multiple causes of converter-driven stability effects, a classification into further categories of fast and slow converter-driven stability is necessary, which is systematically presented in this paper. We further provide a detailed overview on appropriate modelling methods including static, quasi-dynamic and dynamic modelling and their respective applications. Typical analysis methods such as eigenvalue and impedance based analysis are explained and related to the previous modelling approaches. Based on that, a guide to which modelling and analysis method is appropriate for which type of converterdriven stability, is provided. In addition, open and recent research questions with regard to studies on nonlinear analyses of large systems with acceptable computational costs are pointed out.