Vibrations with unknown and/or time-varying frequencies significantly affect the achievable performance of control systems, particularly in precision engineering and manufacturing applications. This paper provides an overview of disturbance-observer-based adaptive vibration rejection schemes; studies several new results in algorithm design; and discusses new applications in semiconductor manufacturing. We show the construction of inverse-model-based controller parameterization and discuss its benefits in decoupled design, algorithm tuning, and parameter adaptation. Also studied are the formulation of recursive least squares and output-error-based adaptation algorithms, as well as their corresponding scopes of applications. Experiments on a wafer scanner testbed in semiconductor manufacturing prove the effectiveness of the algorithm in high-precision motion control. Copyright (c) 2015 John Wiley & Sons, Ltd.