|Abstract:||Vortex-induced vibration (VIV) is a dynamic phenomenon that can occur when there is fluid flow past a bluff body with flexibility. Over time, VIV can cause fatigue damage, so it may be desirable to suppress these vibrations. It is important to understand how the system behaves when trying to control vibrations; a reduced order model may be an effective way to study the system dynamics. Developing a data driven model from simulation and/or experimental results can be difficult, but there are existing phenomenological models that attempt to describe VIV, several of which will be explored in this thesis. These models consist of a structural equation representing a simple sprung bluff body coupled to a wake equation representing the effects of the surrounding fluid on the oscillator; the latter is generally a nonlinear oscillator exhibiting limit cycle behavior. The coupling, structural equation, and type of nonlinearity in the wake equation vary between different models, and the effects of these differences will be explored. The parameters of these equations must be identified, and then results from these models will be compared with the results obtained from a high fidelity CFD simulation to determine the relative quality of each reduced order model. The deficiencies of each model and the effects they produce will also be explored. Finally, the most important traits of each reduced order model will be identified, and, finally, the best reduced order model, with specific parameter values, will be presented.