Floating offshore wind technology is being developed rapidly with the aim of harvesting high-energy wind resources in medium and deep water areas, unreachable using bottomfixed solutions. As floating wind turbines are subject to combined wind and wave excitation in a variety of offshore environmental conditions, a deep interdisciplinary understanding of floater hydrodynamics, turbine aerodynamics and mooring system dynamics is required. Continued research of different design solutions is essential for the future development of floating wind, with tension-leg platforms being an attractive solution due to reduced floater motions, drafts and capital costs. The present thesis explores the dynamic behaviour of different tension-leg platform designs from two standpoints: A closer look: a detailed numerical model of a 10 MW floating wind turbine was built in EDF R&D’s hydro-aeroelastic engineering tool DIEGO to explore the effects of tendon inclination on the system’s response to irregular waves. The interactions of different design solutions with higher-order hydrodynamic loading were investigated by including second- and third-order inertial hydrodynamic loads into the time-domain simulations, capturing low-frequency wave drift forces, springing and ringing effects. The inclusion of quadratic contributions showed that tendon inclination can increase tension variations in the mooring lines when subject to extreme wave climates, potentially leading to slacking in the mooring lines being observed more frequently. This suggests that neglecting higherorder hydrodynamics can lead to underestimations of motion and tendon tension responses of tension-leg platform wind turbines. A step back: the numerical fatigue analysis of floating offshore wind turbines must account for the environmental loading over its design life, with the stochastic nature of the marine climate typically represented by correlated metocean events. In this context, the uncertainties associated to wind-wave correlation techniques were investigated by comparing parametrised representations of metocean climates against high-fidelity wind and wave realisations. A computational method was developed in order to couple offshore wind turbine models with realistic numerical metocean models, referred to as numerical prototype due to the highly realistic marine conditions in which it operates. This method allows the virtual operation of offshore wind turbines anywhere within a considered spatial domain (e.g. the Mediterranean Sea or the North Sea), introducing a range of novel capabilities and unprecedented accuracy. The industrial interest lies in its ability to perform reliable hindcast investigations of existing installations, reducing the uncertainties surrounding the approximations intrinsic to existing damage-equivalent methods.