The literature on reduced-order modeling, simulation, and analysis of the vibration of bladed disks found in gas-turbine engines is reviewed. Applications to system identification and design are also considered. In selectively surveying the literature, an emphasis is placed on key developments in the last decade that have enabled better prediction and understanding of the forced response of mistuned bladed disks, especially with respect to assessing and mitigating the harmful impact of mistuning on blade vibration, stress increases, and attendant high cycle fatigue. Important developments and emerging directions in this research area are highlighted. I. Introduction T URBINE engine rotors, or bladed disks, are rich dynamical systems that are known to suffer from severe vibration problems. Although a bladed disk is typically designed to have identical blades, there are always random deviations among the blades caused by manufacturing tolerances, wear, and other causes. This is called mistuning. Even though mistuning is typically small (e.g., blade natural frequency differences on the order of a few percent of the nominal values), mistuned bladed disks can have drastically larger forced response levels than the ideal, tuned design. The attendant increase in stresses can lead to premature high cycle fatigue (HCF) of the blades. HCF is a major cost, safety, and reliability issue for gas-turbine engines. For example, in 1998 it was estimated by the U.S. Air Force that about 55% of fighter jet engine safety Class A mishaps (over $1 million in damage or loss of aircraft) and 30% of all jet engine maintenance costs were due to HCF. 1 It is clearly of great interest to be able to predict-and, ultimately, to reduce-the maximum blade response as a result of mistuning. The comprehensive modeling, analysis, and understanding of bladed disk vibration is thus critical to reducing the occurrence of HCF and improving the performance and reliability of turbine engines. Bladed disk vibration first received significant attention from the research community in the late 1960s and the 1970s. Notable early work was done by Whitehead, 2 Wagner, 3 Dye and Henry, 4 and Ewins. 5−8 The bladed disk vibration literature has been surveyed by Srinivasan 9,10 and Slater et al. 11 The 1997 survey by Srinivasan 10 Matthew P. Castanier is an Associate Research Scientist in the Department of Mechanical Engineering at the University of Michigan. He received his Ph.D. in Mechanical Engineering from the University of Michigan in 1995. His research interests are in the area of structural dynamics and vibration, including reduced-order modeling, low-to mid-frequency vibration and power flow in complex structures, localization and related phenomena in periodic or cyclic structures, and vibration of mistuned bladed disks in turbine engines. Christophe Pierre is Dean of the Faculty of Engineering at McGill University in Montréal, where he is also Professor of Mechanical Engineering and holds the Canada Research Chair in Structural Dynamics and Vibration. He ...