Abstract: Zernike polynomials, due to their orthogonality and rotational invariance, are widely used in the characterization and optimization of optical surfaces. They can effectively reduce fitting errors and provide high-precision descriptions of complex surfaces with only a few coefficients, contributing to improved imaging quality and simplified performance analysis in optical systems. This paper provides an overview of freeform surface description methods, including both global and local approaches. It discusses the research progress on Zernike polynomials in surface characterization, both domestically and internationally, explores their practical applications in this field, and finally anticipates the future prospects of Zernike polynomials in surface characterization.