Summary: In this paper we provide a review of the state-of-the-art active vibration control of axially moving materials (string and beam, etc.) in the past ten years, with particular regard to the subjects of some important active control methods of axially moving strings. First, an introduction is given to explain the aims and scope of this paper. This is followed by a comprehensive discussion of the active wave control methods presented by many investigators in the past ten years, including feedback control methods (such as the modal control method, the direct velocity feedback control method and the control method via transfer function formulation), active wave control methods combining transfer function, boundary control methods using the Lyapunov function, the variable structure control method, the adaptive control method, the vibration control of an axially moving beam and the active control of a moving material with arbitrarily varying length, etc. Finally, we conclude with a discussion of several issues for future research in this area.