A comprehensive review of modelling techniques for the flow-induced vibration (FIV) of bluff bodies is presented. This phenomenology involves bidirectional fluid–structure interaction (FSI) coupled with non-linear dynamics. In addition to experimental investigations of this phenomenon in wind tunnels and water channels, a number of modelling methodologies have become important in the study of various aspects of the FIV response of bluff bodies. This paper reviews three different approaches for the modelling of FIV phenomenology. Firstly, we consider the mathematical (semi-analytical) modelling of various types of FIV responses: namely, vortex-induced vibration (VIV), galloping, and combined VIV-galloping. Secondly, the conventional numerical modelling of FIV phenomenology involving various computational fluid dynamics (CFD) methodologies is described, namely: direct numerical simulation (DNS), large-eddy simulation (LES), detached-eddy simulation (DES), and Reynolds-averaged Navier–Stokes (RANS) modelling. Emergent machine learning (ML) approaches based on the data-driven methods to model FIV phenomenology are also reviewed (e.g., reduced-order modelling and application of deep neural networks). Following on from this survey of different modelling approaches to address the FIV problem, the application of these approaches to a fluid energy harvesting problem is described in order to highlight these various modelling techniques for the prediction of FIV phenomenon for this problem. Finally, the critical challenges and future directions for conventional and data-driven approaches are discussed. So, in summary, we review the key prevailing trends in the modelling and prediction of the full spectrum of FIV phenomena (e.g., VIV, galloping, VIV-galloping), provide a discussion of the current state of the field, present the current capabilities and limitations and recommend future work to address these limitations (knowledge gaps).