In many real-life and engineering applications flow-induced vibrations play a pivotal role; examples can be taken from various engineering fields like aerospace engineering (e.g. flutter), civil engineering (e.g. vibration in heat exchangers), maritime engineering (e.g. vibration of propeller blades) to name a few. Flow-induced vibration is a phenomenon that is a sub-set of fluid-structure interaction, which considers the (mechanical) interactions between flows and deformable structures. In this lecture, we will discuss the numerical approach that can be taken to model such systems. We use a three-field approach, where the dynamics of the flow, structure, and the flow domain mesh are considered coupled through kinematic and dynamic conditions on the fluid-structure interface. Methods to deform the fluid mesh as well as methods to resolve the spatial and temporal coupling at the fluid-structure interface are discussed. Choices and consequences for one-way or two-way coupling, loose or strong coupling, and absolute or relative mesh motion will be illustrated on the classical elastically mounted cylinder in cross flow, with a particular focus on the (numerical) sources of energy addition/dissipation, that can influence the predicted vibration amplitude, as well as the physical exchange of energy at the fluid-structure interface.