Abstract: Investigations on transverse vibration of axiallymoving strings and its control are reviewed. Transverse vibration of　axially moving strings is involved in many engineering devices such as　power transmission belts, magnetic tapes, paper tapes, thread lines,band saws, and aerial cable tramways. In the context of linear models,besides a few early results, recent studies on modal analysis of moving　strings, vibration of constrained and coupled moving strings, and　parametric vibration of moving strings are summarized. In the context　of nonlinear models, the equations of motion of moving strings withlarge amplitude are presented, and new progresses on discretizated and　direct approximate analytical analysis, modeling of damping mechanisms　as viscoelastic materials, and coupled vibration of power transmission　systems are surveyed. The state-of-the-art in active control of moving　strings vibration, including controllability and observability, the　frequency domain analysis and the energy analysis, adaptive vibration　control, and nonlinear vibration control, is discussed. Some topics forfuture research, such as nonlinear dynamical behavior of movingstrings, vibration of moving viscoelastic strings, control of hybrid　systems containing moving strings and control of nonlinear oscillations　of moving strings, are suggested.