As mentioned earlier, one of the challenges in history matching and field development optimization under geological uncertainty is the high computational cost of the process. The majority of the computational burden is associated with numerous reservoir simulations required to calculate the misfit/objective function over a large number of realizations. In addition to reducing the number of geological scenarios, another way to reduce the computational cost associated with history matching (HM) and robust optimization (RO) under geological uncertainty is to use proxy models. Proxy models are simpler models than the full-physics reservoir simulation with ignorable computational costs compared to reservoir simulation. These models can substitute the reservoir simulator to speed up the computation of the misfit/objective function. This chapter is dedicated to introducing proxy models used in history matching and robust field development optimization. Different kinds of proxy models; such as physics-based, non-physics-based, and hybrid proxies; pros and cons of using proxy models; and some example applications of proxy models are introduced.