Abstract: The periodic structures have been widely spread in the array antenna, frequency selective surface and metamaterial fields. The fast computational algorithm for electromagnetic scattering and radiation from large-scale and finite periodic structures (LFPSs) has always been a hot and difficult subject in computational electromagnetics (CEM) field. In this paper, we review some significant approaches within the moment method for analysis of the LFPSs and provid the comparison among these approaches. In addition, we discuss the future direction of the development in CEM for analysis of the LFPSs.