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We review the Space Mapping (SM) concept and its applications in engineering optimization and modeling. The aim of SM is to avoid computationally expensive calculations encountered in simulating an engineering system. The existence of less accurate but fast physically-based models is exploited. SM drives the optimization iterates of the time-intensive model using the fast model. Several algorithms have been developed for SM optimization, including the original SM algorithm, Aggressive Space Mapping (ASM), Trust Region Aggressive Space Mapping (TRASM) and Hybrid Aggressive Space Mapping (HASM). An essential subproblem of any SM based optimization algorithm is parameter extraction. The uniqueness of this optimization subproblem has been crucial to the success of SM optimization. Different approaches to enhance the uniqueness are reviewed. We also discuss new developments in …