Functionally graded materials (FGM) are increasingly used in the engineering field. In many applications, FGMs are modelled as plates. Plates made of functionally graded materials (FGPs) are mostly designed to perform under elevated temperatures. In those circumstances, they are often under the combined effect of thermal and mechanical loads. There have been many studies on buckling analysis of FGP under either mechanical or thermal loads; however, only a few studies have addressed the combined effect of both loads acting together. This article focuses on the review of research on buckling analysis of FGP under the combined thermal and mechanical loads.