In recent years, the offshore wind industry has experienced significant growth with the installation of offshore wind farms in shallow water (such as in Denmark). However, almost all of offshore wind turbines to date are mounted on fixed-bottom support structures in water depths of less than 50m, which are not feasible off the coasts of the United States, China, Japan, Norway and Spain, among others. As a potential solution, wind turbines can be mounted on floating support structures anchored to the seabed through the mooring lines to restrain the global movement of the platform against the effects of wind, waves and currents. Usually, the mooring systems of floaters can be designed such that the system's natural periods fall outside the range of common wave periods. However, due to nonlinearity in the wave to force transformation, oscillating forces can still arise in period ranges that will cause resonance in the structure. In general, the dynamic loads should be studied for the primary components of the wind turbine (blades, drivetrain, nacelle and tower), and also for the mooring systems in floating support structures. One of the main challenges is to reduce the fatigue of a floating offshore wind turbine so as to guarantee its proper functioning under the constraints imposed by the floating support structures subject to a greater range of motion than that of the fixed-bottom support structures. This paper will analyze the loads and dynamic response of floating support structures together with the mooring systems and will address the structural control issues on the mitigation of the dynamic wind and wave loads on floating wind turbines.