In this paper, we review frequency domain techniques for computing unsteady flows in turbomachinery. The frequency domain approaches, which can be used to model both small-disturbance and nonlinear time periodic flows, are computationally very efficient, typically one to two orders of magnitude more efficient than time domain techniques. Furthermore, they can be used to analyze a wide variety of aeromechanic, performance, unsteady heat transfer, and flow stability problems in turbomachinery, including the important problem of unsteady flows in multistage machines. © 2003 by Kenneth C. Hall, Jeffrey P. Thomas, Kivanc Ekici, Dmytro Voytovych. Published by the American Institute of Aeronautics and Astronautics, Inc.