Fishnet metamaterials are nowadays the best candidates to accomplish some suggestive physical phenomena like negative refractive index, super-lenses, cloaking devices, nano antennas, etc. This work summarizes the study of the propagation of electromagnetic waves in periodic structures, namely Fishnet metamaterials, in the optic range. A full presentation of the phenomenology involved and of the numerical methods commonly used for the physical investigation is therefore the purpose of this work. Indeed it represents a useful text book for all those who first begin the research field in negative regractive index metamaterials and want to learn more about their uncommon properties and their application in future optic devices.