In this paper, we review some recent developments for computing unsteady aerodynamic loads associated with turbomachinery aeromechanics. In particular, we example the use of 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 at least one order 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. We show a number of novel uses of frequency domain techniques including their use to model nonlinear flows, multistage flows, and self-excited non-synchronous fluid instabilities.