This paper reviews the progress made during the past decade on vortex-induced vibration (VIV) of long slender cylindrical structures. When the aspect ratio, which is defined as the ratio of length to diameter for cylindrical structures, is large enough (10²–10³), some unexpected phenomena occur, e.g., dual resonance, multi-mode vibration, unsteady lock-in, the third and higher harmonic fluid forces and traveling wave dominant response, as summarized in this paper. In addition, a brief outline is given of numerical methods used in predicting the response of long slender cylinder undergoing VIV.