The applications of numerical simulation modeling such as assisted history matching, production optimization, and reservoir performance forecasting usually lead to significant time, computer resources, and accordingly huge associated costs. To overcome these circumstances, proxy modeling is the suggested approach to deliver a cheap alternative and approximate nonlinear oil and gas reservoir responses such as recovery factor and reservoir operating parameters and characteristics. Proxy modeling is considered a powerful tool for optimization and uncertainty analysis alike. Conventionally, the reservoir simulation is solved by tuning selected uncertain reservoir parameters one at a time. While, the most important feature of proxy modeling is the ability to determine the combined effect of uncertain parameters at the same time. Petroleum engineering field usually requires a wide variety of parameter estimation problems, and proxy modeling can satisfy this demand. Proxy modeling can be developed based on different methods; the current paper presents a comprehensive review of the methods of developing of proxy modeling and their applications in reservoir simulation since proxy modeling is becoming more widely used as a simplify highly complex substitution to reservoir simulation with reasonable accuracy. This article reviews the methods used in recent years to develop proxy models as a successful replica of complex numerical flow simulation models. This will shed the light of different proxy models, their uses, and how to judge on their efficiencies. © 2019, Saudi Society for Geosciences.