The book explores Kriging metamodeling for interpolation, sensitivity analysis and optimization of simulation models with costly computational expenses. A novel Kriging model is developed and named Taylor Kriging (TK) where Taylor expansion is used to identify a drift function. Taylor expansion has the excellent nonlinear approximation capability, thus enhancing the interpolation capability of Kriging. Sample standard deviation is used as the metric for influence distance in a covariance function of Kriging, and makes simulations with data of differing magnitudes have a consistent measure unit. The partial differentiation equation of Kriging is developed and used together with analysis of variance to assist in sensitivity analysis on a simulation model. A novel simulation optimization algorithm named SOAKEA is created which integrates Kriging with evolutionary algorithms to optimize simulation models with expensive running cost. The properties of SOAKEA are investigated, and some empirical conclusions are obtained. In addition, the Kriging software is developed in order to satisfy the needs of wide applications.