The design and development of floating offshore wind turbines (FOWTs) is an attractive issue in the wind energy harvesting field. In this study, the research related to the high-fidelity computational fluid dynamic simulations of FOWTs is comprehensively summarized and analyzed. Specifically, the component-level studies including aerodynamics, aeroelasticity and hydrodynamics are presented. The system studies with increasing complexity are performed, such as the simplified aerodynamics, prescribed platform motions and fully coupled aero-hydrodynamics, as well as a little knowledge relevant to the aero-hydro-elastic behaviors. This study emphasizes that some efforts should shift to the research on strongly coupled aero-hydro-elastic performance of FOWTs with the increasing rotor diameter. Moreover, further investigations of more realistic atmospheric inflows and strong interactions between multi-FOWTs are required. This study aims to introduce the hotspots of high-fidelity simulations of FOWTs to novel researchers, as well as to provide some suggested solutions.