Tidal energy, characterized by its widespread distribution and immense reserves, stands as a promising renewable energy source suitable for large-scale development and utilization. Flow-induced vibration, a common fluid-structure interaction phenomenon, facilitates efficient energy conversion at lower flow velocities through the vibration of cylindrical structures. Energy harvesting technologies based on flow-induced vibration of cylindrical structures exhibit significant potential for wide-ranging engineering applications in the future. In recent years, numerous experimental and numerical simulation studies have been conducted to explore the flow-induced vibration characteristics and energy harvesting performance of cylinder structures. This paper comprehensively presents the research progress in the theoretical and technical aspects of flow-induced vibration energy harvesting for various cross-sectional forms of single cylinder and cylinder arrays. For the case of flow-induced vibration energy harvesting from a single cylinder, substantial progress has been made in elucidating the influence patterns of passive turbulence controllers, system damping, Reynolds number and boundary conditions on energy harvesting performance. Theoretical foundations and technological advancements have been preliminarily established. Concerning the energy harvesting from a non-circular cross-sectional cylinder, the paper outlines the preliminary understanding of the flow-induced vibration mechanisms and energy harvesting capabilities of triangular, quadrilateral, polygonal and irregularly shaped cylinder under specific conditions such as incoming flow angle, system mass ratio, system damping, system stiffness, and Reynolds number. In the context of flow-induced vibration energy harvesting from cylinder arrays, the interference of flow fields between cylinder oscillators necessitates a rational design of parameters such as cylinder arrangement, cylinder spacing and system damping to achieve maximized fluidic energy capture. By reviewing the domestic and international research progress in flow-induced vibration energy harvesting theories and technologies, this paper provides a prospective outlook for future studies, aiming to stimulate the development of flow-induced vibration energy harvesting theories and advance the engineering applications of flow-induced vibration energy conversion devices.