Abstract: Functionally graded materials (FGMs) are categorized as functional composites, where the volume fractions of two or more materials change continuously based on position along specific dimensions (mainly through-the -thickness) of the structure to achieve desired functionality. A typical example of FGM is an inhomogeneous composite consisting of distinct phases of material constituents (e.g., ceramics and metals for thermal barrier structures), featuring a strong bending-stretching coupling effect. The overall properties of FGMs are unique and distinguishable from the individual materials comprising them. Mechanical properties exhibit continuous variation across the plate thickness. Variations in constituent volume fractions lead to diverse microstructures. The effective properties of FGM plates are assumed to change along the thickness direction, following power law, sigmoid, and exponential distributions. FGMs are created by altering chemical composition, microstructure, or design features from one end to the other as required. They exhibit high-temperature resistance, efficiently mitigating thermal stresses and moisture impacts. The variation in volume fraction throughout the thickness is computed using different homogenization techniques, namely the rule of mixtures, Mori-Tanaka scheme, and self-consistent method. Several micromechanical models have been developed and utilized to estimate effective properties of these materials in relation to volume fraction distributions. The manipulated variable concerns the concentration of reinforcing particles at various points within the component. This study delves into various methods and theories for modeling and analyzing functionally graded materials, offering a comprehensive exploration of their features. The outcomes and new findings of this analysis are presented.