In this paper we present our aerodynamics and fluid–structure interaction (FSI) computational techniques that enable dynamic, fully coupled, 3D FSI simulation of wind turbines at full scale, and in the presence of the nacelle and tower (i.e., simulation of the “full machine”). For the interaction of wind and flexible blades we employ a nonmatching interface discretization approach, where the aerodynamics is computed using a low-order finite-element-based ALE-VMS technique, while the rotor blades are modeled as thin composite shells discretized using NURBS-based isogeometric analysis (IGA). We find that coupling FEM and IGA in this manner gives a good combination of efficiency, accuracy, and flexibility of the computational procedures for wind turbine FSI. The interaction between the rotor and tower is handled using a non-overlapping sliding-interface approach, where both moving- and stationary-domain formulations of aerodynamics are employed. At the fluid–structure and sliding interfaces, the kinematic and traction continuity is enforced weakly, which is a key ingredient of the proposed numerical methodology. We present several simulations of a three-blade 5~MW wind turbine, with and without the tower. We find that, in the case of no tower, the presence of the sliding interface has no effect on the prediction of aerodynamic loads on the rotor. From this we conclude that weak enforcement of the kinematics gives just as accurate results as the strong enforcement, and thus enables the simulation of rotor–tower interaction (as well as other applications involving mechanical components in relative motion). We also find that the blade passing the tower produces a 10–12 % drop (per blade) in the aerodynamic torque. We feel this finding may be important when it comes to the fatigue-life analysis and prediction for wind turbine blades.