This survey paper presents and overview on eigenstructure assignment (EA) control design methodologies. EA is an excellent control design method which may be used to assign the entire eigenstructure(eigenvalues, and right or left eigenvectors) of a closed-loop linear system via a full state or an output feedback control law. In general, EA is well-sutied for incorporating classical specifications on damping, settling time, and mode or disturbance decoupling into a modern multivariable control framework. The purpose of this paper is to provide an extensive survey on EA control design methods that might serve as an introduction to a study on EA. The fundamental concepts and formulations for understanding EA problems are extensively described. The recently reported results on EA are also presented.