Through the review of the history of the grating electromagnetic theory, the development process and present situation of electromagnetic theory of one-dimensional diffraction grating development are introduced. Comparing the parameters between one-dimensional gratings and dual-period diffraction grating and researching on the several examples, figuring out that in contrast to one-dimensional diffraction grating, the dual-period diffraction gratings has more excellent performance in application; And watching results of simulating of two kinds of grating show that the theory of dual-period diffraction grating development is not mature enough,which is not as the theory of one-dimensional grating, to apply on research of characteristics and design of grating as a ideal tool. Finally based on the comparison in varieties of electromagnetic theory of dual-period grating,present situation and the prospect of the theory development of double periodic grating are presented.