This article reviews Kriging metamodeling in simulation, a method originally developed in geostatistics for spatial correlation modeling. Kriging is contrasted with classic linear regression metamodels, emphasizing its global nature and ability to handle both deterministic and random simulation models. The article covers the basic assumptions and formulas of Kriging, including the linear predictor and the optimal weights that minimize the Mean Squared Errors (MSE) of the predictor. It discusses the importance of estimating the correlation function and optimal weights, which are crucial for accurate predictions. The article also explores recent extensions of Kriging, such as its application to random simulation and the use of bootstrapping to estimate the variance of the Kriging predictor. Additionally, it reviews one-shot and sequential statistical designs for simulation experiments, including Latin Hypercube Sampling and sequentialized designs. The article concludes with a discussion of future research directions, highlighting the need for improved software and the exploration of alternative criteria for model selection.This article reviews Kriging metamodeling in simulation, a method originally developed in geostatistics for spatial correlation modeling. Kriging is contrasted with classic linear regression metamodels, emphasizing its global nature and ability to handle both deterministic and random simulation models. The article covers the basic assumptions and formulas of Kriging, including the linear predictor and the optimal weights that minimize the Mean Squared Errors (MSE) of the predictor. It discusses the importance of estimating the correlation function and optimal weights, which are crucial for accurate predictions. The article also explores recent extensions of Kriging, such as its application to random simulation and the use of bootstrapping to estimate the variance of the Kriging predictor. Additionally, it reviews one-shot and sequential statistical designs for simulation experiments, including Latin Hypercube Sampling and sequentialized designs. The article concludes with a discussion of future research directions, highlighting the need for improved software and the exploration of alternative criteria for model selection.