This paper provides a state-of-the-art review of eigenstructure assignment methods for vibration cancellation. Eigenstructure assignment techniques have been widely used during the past three decades for vibration suppression in structures, especially in large space structures. These methods work similar to mode localization in which global vibrations are managed such that they remain localized within the structure. Such localization would help reducing vibrations more effectively than other methods of vibration cancellation, by virtue of confining the vibrations close to the source of disturbance. The common objective of different methods of eigenstructure assignment is to provide controller design freedom beyond pole placement, and define appropriate shapes for the eigenvectors of the systems. These methods; however, offer a large and complex design space of options that can often overwhelm the control designer. Recent developments in orthogonal eigenstructure control offers a significant simplification of the design task while allowing some experience-based design freedom. The majority of the papers from the past three decades in structural vibration cancellation using eigenstructure assignment methods are reviewed, along with recent studies that introduce new developments in eigenstructure assignment techniques.