This paper provides a survey of actuator and sensor placement problems from a wide range of engineering disciplines and a variety of applications. Combinatorial optimization methods are recommended as a means for identifying sets of actuators and sensors that maximize performance. Several sample applications from NASA Langley Research Center, such as active structural acoustic control, are covered in detail. Laboratory and flight tests of these applications indicate that actuator and sensor placement methods are effective and important. Lessons learned in solving these optimization problems can guide future research. Padula, Sharon L. and Kincaid, Rex K. Langley Research Center NASA/TM-1999-209126, L-17839, NAS 1.15:209126