The digital twin is an emerging and vital technology for digital transformation and intelligent upgrade. Driven by data and model, the digital twin can perform monitoring, simulation, prediction, optimization, and so on. Specifically, the digital twin modeling is the core for accurate portrayal of the physical entity, which enables the digital twin to deliver the functional services and satisfy the application requirements. Therefore, this paper provides systematic research of current studies on the digital twin modeling. Since the digital twin model is a faithful reflection of the digital twin modeling performance, a comprehensive and insightful analysis of digital twin models is given first from the perspective of the application field, hierarchy, discipline, dimension, universality, and functionality. Based on the analysis of digital twin models, current studies on the digital twin modeling are classified and analyzed according to the six modeling aspects within the digital twin modeling theoretical system proposed in our previous work. Meanwhile, enabling technologies and tools for the digital twin modeling are investigated and summarized. Finally, observations and future research recommendations are presented. •Provide a systematic analysis of currently available digital twin models from multiple perspectives.•Give a complete summary of the whole digital twin modeling process from multiple aspects.•Research the enabling technologies and tools applied in each aspect of the digital twin modeling.•Recommend future research orientations of the digital twin model and modeling.•Propose prospective approaches to resolve the existing problems and emerging challenges.