One of the keys to the success of the fourth industrial revolution (Industry 4.0) is to empower machinery with cyber−physical systems connectivity. The digital twin (DT) offers a promising solution to tackle the challenges for realizing digital and smart manufacturing which has been successfully projected in many scenes. Electrical machines and drive systems, as the core power providers in many appliances and industrial equipment, are supposed to be reinforced on the verge of Industry 4.0 in the fields of design optimization, fault prognostic and coordinated control. Therefore, this paper aims to investigate the DT modelling method and the applications in electrical drive systems. Firstly, taking the high-speed permanent-magnet machine drive system as an example, multi-disciplinary design fundamentals and technologies, aiming at building initial mechanism and simulation models, are reviewed. The state-of-the-art of DT technologies is figured out to serve for high-precision and multi-scale dynamic modelling, by which a framework for DT models of electrical drive systems is presented. More importantly, fault diagnosis and optimization strategies of electrical drive systems in the decision and application layer are also discussed for the DT models, followed by the conclusions presenting open questions and possible directions.