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The uncertainty of geological composition, the invisibility of the under-well real-time working conditions, and the complexity of the engineering simulation in the oil and gas field drilling and production process have hindered its scientific and efficient design and construction. The digital twin technology can bring up real-time, intelligent, and visualized project design and decision-making but has yet to lack a systematic method for modeling oil and gas field drilling and production. In this regard, the article first explored the current levels of investigation and implementation both domestically and abroad, based on that the level of development by applying the maturity index was quantified. It then proposed the digital twin modeling approach for drilling and production in the oil and gas field, which encompassed the modeling workflow, model division strategies, architecture for model assembly and integration, and modeling tools for constructing the digital twin. Also, two case were studied for drilling and production, using wellbore stability while drilling and offshore gas well production system as two examples, respectively. Finally, the difficulties and challenges related to the digital twin deployment in the field were analyzed, based on which the suggestions for its future development are proposed. It is found that the digital twin for drilling and production has stayed at the visualization level and at a relatively low degree of maturity compared to the manufacturing field on digital twin. The complex demand for oil and gas drilling and production systems can be divided into several clear and easy realized sub-demands. Based on requirement analysis, the modeled object can be separated to be various sub-models based on the granularity, dimension, and lifecycle. The sub-models are then assembled layer by layer across the model, function, and demand layers so that the multi-dimension and multi-field models can be integrated. Meanwhile, an improvement of their methods and an increase in efficiency for the model administration, data management, and engineering simulation ae desired. Moreover, the digital twin faces the problems such as difficulty in selection and fusion of multi-source heterogeneous data, vagueness in the sub-model definition, and ambiguity in the model validation, as well as the challenges such as the complicated kinetics processes, multi-division and multi-task collaboration, and development of domestic software tools. In summary, the digital twin modeling approach and the case studies in this article can provide a methodological guidance and practical reference for oil and gas drilling and production practices.