Abstract Vortex-induced vibration (VIV) is a well-known phenomenon in the fields of physics and engineering. However, the description on vortex-shedding from a flexible or an elastically restrained cylinder (such as a deepwater riser or a floater) is somewhat primitive. When such a structure experiences flowing fluids, the pressure build-up at the stagnation point near the leading edge is automatically assumed by many. As a result, the vortex-shedding theories on stationary cylinders have been applied to the compliant structures without modification. It is believed that the lack of a sound understanding and explanation of this complex hydroelastic phenomenon has, to a certain degree, hindered VIV research and design. Based on VIV tests and test data, the author proposes a revised interpretation of VIV for the widely used compliant structures in offshore and marine engineering. The VIV process is first examined; starting from the instant the flow encounters the structure. The key events leading to VIV are identified and the relations among them are explored, such as that between the deflection and vortex-shedding. A new parameter characterizing a structure, termed as the coefficient of compliance, is then introduced. Its impacts on a number of VIV response parameters are qualitatively described. Along this line, the issues on VIV experiment, computer simulation, and VIV design are briefly discussed. Ideas on further research and development are suggested. The purpose of this paper is to highlight the effects of the structural compliance on VIV, and provoke others to look into these important influences, so that the VIV design can be established on a more solid foundation.