Recent state-of-art applications of diffraction gratings and stratifie
d materials with one or several modulated interfaces impose specific r
equirements on electromagnetic grating theory. A review of such applic
ations is presented here with an emphasis on the aspects of the theore
tical methods required for their efficiency prediction and optimizatio
n. A brief review of the basic ideas of the various electromagnetic th
eories used is given. The specific domain of validity for each theory
is discussed together with advantages and shortcomings. The aim is to
serve as a guide in selecting the most appropriate theoretical method
for handling specific grating problems.