In the past, robotic manipulators, machine tools, measurement devices, and other systems were designed with rigid structures and operated at relatively low speeds. With a growing demand for fuel efficiency, smaller actuators, and speed, lighter weight materials are increasingly used in many systems, making them more flexible. Achieving high-performance control of flexible structures is a difficult task, but one that is now critical to the success of many important applications, such as atomic force microscopes, disk drives, tape drives, robotic manipulators, gantry cranes, wind turbines, satellites, and the space station remote manipulator system. The unwanted vibration that results from maneuvering or controlling a flexible structure often dictates limiting factors in the performance of the system. Over the last few decades, many feedback, feedforward, and combined feedforward/feedback control methods have been developed for flexible structures. We will discuss and compare several of these control methods in conjunction with overviewing some of the issues in the modeling of flexible structures, and we will highlight a few recurring themes across the diverse application areas mentioned above.