To study the specific impact of optical elements on the performance of optical systems, Zernike polynomials are employed as analytical tools for performance evaluation. The optimization methods for optical elements and the theoretical foundation of Zernike polynomials are begun with, introducing the concepts of circular Zernike polynomials and annular Zernike polynomials. It also explores the relationship between circular Zernike polynomials and Seidel aberrations, as well as their application in wavefront fitting. A review of research achievements both domestically and internationally in the optimization of optical element surface shapes, structural optimization, and system imaging performance is presented, showcasing the role of Zernike polynomials in these areas. Furthermore, a analysis of the key factors influencing the optimization of optical elements is provided, highlighting how these factors affect the optimization results of Zernike polynomials. Finally, the development trends of Zernike polynomials in the optimization of optical elements are anticipated.