This article reviews Kriging metamodeling in simulation. It presents the basic assumptions and formulas of Kriging, contrasting it with classic linear regression metamodels. It extends Kriging to random simulation and discusses bootstrapping to estimate the variance of the Kriging predictor. It also reviews sequentialized and customized designs for simulation experiments. The article concludes with topics for future research. Kriging, originally developed in geostatistics by Danie Krige, is a method used for interpolation and prediction. It assumes a stationary covariance process, where the correlation between outputs depends on the distance between inputs. Kriging models are global rather than local and are used for prediction, with goals including sensitivity analysis and optimization. The article discusses the use of Kriging in both deterministic and random simulations. In deterministic simulations, Kriging is used for interpolation, while in random simulations, it is applied to predict outputs with uncertainty. The article also covers methods for estimating the variance of the Kriging predictor, including bootstrapping and cross-validation. The article reviews various statistical designs for simulation experiments, including Latin Hypercube Sampling (LHS) and sequentialized designs. Sequential designs are more efficient as they require fewer observations and adapt to the simulation results. The article also discusses the use of Kriging in practical random simulation models and the need for further research in this area. Key topics include the robustness of Kriging in random simulations with heterogeneous variances, the application of Kriging to multivariate outputs, and the integration of Kriging with other metamodeling techniques. The article emphasizes the importance of designing simulations that account for the properties of the underlying simulation model, such as monotonicity. Future research directions include improving Kriging software, developing asymptotic proofs for sequential designs, and applying Kriging to more complex simulation models.This article reviews Kriging metamodeling in simulation. It presents the basic assumptions and formulas of Kriging, contrasting it with classic linear regression metamodels. It extends Kriging to random simulation and discusses bootstrapping to estimate the variance of the Kriging predictor. It also reviews sequentialized and customized designs for simulation experiments. The article concludes with topics for future research. Kriging, originally developed in geostatistics by Danie Krige, is a method used for interpolation and prediction. It assumes a stationary covariance process, where the correlation between outputs depends on the distance between inputs. Kriging models are global rather than local and are used for prediction, with goals including sensitivity analysis and optimization. The article discusses the use of Kriging in both deterministic and random simulations. In deterministic simulations, Kriging is used for interpolation, while in random simulations, it is applied to predict outputs with uncertainty. The article also covers methods for estimating the variance of the Kriging predictor, including bootstrapping and cross-validation. The article reviews various statistical designs for simulation experiments, including Latin Hypercube Sampling (LHS) and sequentialized designs. Sequential designs are more efficient as they require fewer observations and adapt to the simulation results. The article also discusses the use of Kriging in practical random simulation models and the need for further research in this area. Key topics include the robustness of Kriging in random simulations with heterogeneous variances, the application of Kriging to multivariate outputs, and the integration of Kriging with other metamodeling techniques. The article emphasizes the importance of designing simulations that account for the properties of the underlying simulation model, such as monotonicity. Future research directions include improving Kriging software, developing asymptotic proofs for sequential designs, and applying Kriging to more complex simulation models.