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 structure. It provides the numerical analysis of reflectarray antenna and a comparison with parabolic reflectors using the software package CDT. it considered] aspects to the characterization of the cell unit in an infinite periodic environment, and hence, simulation of the whole reflectarray. Finally, it introduces two designs for X-Band reflectarray antennas. The first one is designed to produce pencil beam at broadside direction by using cylindrical dielectric resonator antennas at 12 GHz and the other reflectarray is designed to produce beam steering.