In this paper, starting from the “double-high” characteristics of power grid becoming more and more prominent, resulting in the increasing demand for related measurement and the corresponding increase in measurement requirements, It comprehensively summarizes and sorts out the researchs achievements on iteration, expansion and updating of synchronous phasor measurement algorithms, including the principles, accuracy, responsiveness, and applicability as well as adjustability of the synchronous fundamental, harmonic, and inter-harmonic phasor measurement algorithms. Simultaneously, we review the latest progress in optimizing the dynamic performance of the above algorithms under the complex power grid environment, which aims to achieve anti-interference capability, dynamic performance, and accuracy to meet the practical needs and relevant standards.