This work presents the basic theory of reflectarray antenna and a survey of its historical developments and future prospects. Then, an overview of its challenges like bandwidth enhancement methods, reconfigurability, and beam scanning techniques are introduced. Also it provides a survey of different techniques to analyze reflectarray antenna and focus on using electric field integral equations (èfie) in the solution using methods of analysis with a subsequent moment in the spectral domain. It introduces a fast analytical technique to analyze the problem of reflectarray as a periodic array...