This review article summarizes the development of higher order theories for the dynamic analysis of piezoelectric plates, and describes their applications, especially for crystal resonators. The theories are categorized according to how the displacement components and electric potential are assumed to vary through the plate thickness. The greatest attention has been given to ordinary polynomial variations, especially the efforts of RD Mindlin and HF Tiersten and their coworkers. Considerable progress has also been made using trigonometric series representations, especially by PCY Lee and his coworkers. Legendre polynomial and normal mode expansions have also been developed. Both analytical and finite element methods of dealing with problems are described. The article contains 174 references.