This paper presents a review of the state of the art of proxy models application in the oil and gas industry from upstream, midstream, and downstream. The focus on proxy models is because they are the pillar of the digital twins. They compensate for the slow response of the numerical simulation models. Proxy models can get updated very quickly with new data compared to numerical models. The proxy models apply to cross-disciplines such as fluid mechanics, thermodynamics, and electronics. Proxy models are tools for the swift response to the process events when the cost of decision time is high. The history of the proxy model is discussed first followed by a review of the literature. First, a literature review and the history of the proxy model are covered. The objectives and uses of proxy models are then thoroughly described while the evolution and development process of proxy models are detailed. A few proxy model examples are provided to emphasize the significance of the proxy model and technical advancement. Regression, artificial neural networks, fuzzy logic, and support vector machines are the major approaches for delivering proxy models. Each method's strengths and drawbacks are addressed. These case studies show the need for data cleansing, data transformation to the appropriate domain, and a precise model verification and validation strategy for creating a trustworthy proxy model. Industry-wide, the gaps, and difficulties are addressed, including data accessibility, workflow, model health check, operability, and model uncertainty. A review of proxy models revealed that both technical solution acceptance and workflow robustness have greatly increased at the maturity level in proxy model applications in the oil and gas industry. However, the typical workflow is not being used, and many case studies show that crucial steps like verification and validation are not being taken. The key issue identified in the review was that proxy models are derived from analytical and numerical models, which is in contrast to proxy models, which by their nature rely on the data at hand to inform predictions and optimizations. The astounding potential of proxy models in prediction and optimization is still untapped, and more research is needed to improve model quality, incorporate data into the core of the proxy models, increase their robustness, and develop robust performance metrics to address and evaluate the performance, dependability, and timeliness of the proxy models. Currently, proxy models are secondary tools for optimization of the processes and decision making, while in the future outlook is to be the main tool not only in daily surveillance and monitoring but for the optimization process. In this paper, a best practice workflow for the proxy model is proposed for the oil and gas industry. The evolution of proxy models and their level of complexity is reviewed. Most published work on proxy models is built based on the synthetic data and simulation model output. In the applied workflow, most model validation and verification are missed or ignored. Except for a few published works on the real-time usage, the models are barely connected to real-time and they are used for static decision-making process other than real-time usage.