In recent years use of the nonconventional type of machines is increasing due to some limitations of the conventional type of machines. Electric discharge machine is one of the nonconventional types of the machine generally used for cutting an intricate shape from the hard work piece. Variation in process parameters of electric discharge machining affects its response variable like material removal rate, surface finish, recast layer, wear ratio etc. Because, of that for getting good results of response variables its necessary that proper selection of response of variable. Many researchers tried to optimize process parameters of electric discharge machining with the help of Taguchi method and Grey relational analysis for getting acceptable results of the response variable. Researchers use the Taguchi method for single objective optimization and grey relational analysis for multi-objective optimization. The main focus is on optimization of process parameters of EDM and its modified versions like WEDM, Micro-EDM and PMEDM using Taguchi method and Grey relational analysis and hence, only such research works are included in this review. Where the Taguchi method and Grey relational analysis method is used to optimizing process parameters of EDM; that were published in the last 15 years since 2003. The review work on such large extent was not tried earlier by considering this optimization process for EDM and its modified versions and hence this review work may become ready information at on a place and help researchers to decide their direction of research.