Flow-induced vibration (FIV) in nuclear reactor vessels has been extensively studied during the mechanical design of reactor vessels. Many power plants have increased the interest in coupled modern fluid and solid mechanics codes to facilitate the understanding of the phenomena causing damage to components termed fluid–structure interaction (FSI). A better understanding of these structure interactions is critical for enhancing safety, minimizing radiation risks, improving public health and safety, and fostering innovation in the nuclear industry. Furthermore, it supports nuclear energy as a clean alternative to fossil fuels, contributing to the reduction of global carbon emissions and advancing responsible production and consumption. Pressure wave propagation, acoustic resonance, flow-induced turbulence, and fluid-elastic instability are the four types of FSI-coupled systems that are investigated in this work. Different computational methods are presented to simulate FSI problems and should be selected depending on the physical complexity of the problems. One-way FSI where Computational Fluid Dynamics (CFD) or thermal-hydraulics results are applied on a structural model is common, while FSI calculations with iterative fluid–structure simulations will be more and more available with the increase in computer capacity and the development of a more cost-effective turbulence model. Most modeling results have resulted in errors in the range of ± 10% with the experimental data; however, in some cases, the choice of a different boundary condition has been shown to result in up to 30% errors.