A brief overview of vortex-induced vibration (VIV) of bridge decks is presented, highlighting special VIV features concerning bridge decks. A popular VIV model (Van der Pol-type model) for bridge decks is examined in detail. Alternatively, a truncated Volterra series-based nonlinear oscillator is introduced to model the VIV system. Typical features of VIV such as the limit cycle oscillation (LCO), frequency shift, hysteresis, and beat phenomenon are parsimoniously and accurately captured in the proposed nonlinear model. As a functional expansion of a nonlinear system, the Volterra series is convenient for estimating the linear and nonlinear contributions to VIV. It is demonstrated that the relative contribution of nonlinear effects in VIV is around 50% of the total response for a range of bridge cross sections. The efficacy of the Volterra series as a reduced-order model (ROM) in capturing aerodynamic nonlinearities eliminates the need for reliance on conventional phenomenological models as it promises to offer a unified framework for nonlinear wind effects on long-span bridgesfor example, VIV, buffeting, and flutter. (C) 2013 American Society of Civil Engineers.