Recently, more wind turbine systems have been installed in deep waters far from the coast. Several concepts of floating wind turbine systems (FWTS) have been developed, among which, the semi-submersible platform—due to its applicability in different water depths, good hydrodynamic performance, and facility in the installation process—constitutes the most explored technology compared to the others. However, a significant obstacle to the industrialization of this technology is the design of a cost-effective FWTS, which can be achieved by optimizing the geometry, size, and weight of the floating platform, together with the mooring system. This is only possible by selecting a method capable of accurately analyzing the FWTS-coupled hydro–aero–structural dynamics at each design stage. Accordingly, this paper provides a detailed overview of the most commonly coupled numerical and physical methods—including their basic assumptions, formulations, limitations, and costs used for analyzing the dynamics of FWTS, mainly those supported by a semi-submersible—to assist in the choice of the most suitable method at each design phase of the FWTS. Finally, this article discusses possible future research directions to address the challenges in modeling FWTS dynamics that persist to date.