Abstract.Material engineering has become one of the corner stones in various engineering applications. The scientific alteration of base materials into various inorganic and organic compounds has resulted in the development of Functionally Graded Material (FGM). FGM can be described as a cutting edge material in which the particular material's properties could be made varied as the dimension changes. The aims of this study was to review on FGM's applications and its manufacturing processes. In addition, the mathematical idealization of the FGM was also reviewed. Based on the review, since FGMs are highly heterogeneous, it can be idealized as their mechanical properties changes smoothly with respect to their spatial coordinates. Nonetheless, in order to analyze FGMS in an efficient manner, the homogenization schemes are needed to be simplified from their complicated heterogeneous microstructures. Closed-form solutions of some fundamental solid mechanics' problems can be obtained by this idealization. Conclusively, FGM is unique in relation to any of the individual materials that structures it. Suggestively, this provide a limitless possibility for future engineering applications.