We provide an overview of the aerodynamic and FSI analysis of wind turbines the first three authors' teams carried out in recent years with the ALE-VMS and ST-VMS methods. The ALE-VMS method is the variational multiscale version of the Arbitrary Lagrangian-Eulerian (ALE) method. The VMS components are from the residual-based VMS (RBVMS) method. The ST-VMS method is the VMS version of the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) method. The techniques complementing these core methods include weak enforcement of the essential boundary conditions, NURBS-based isogeometric analysis, using NURBS basis functions in temporal representation of the rotor motion, mesh motion and also in remeshing, rotation representation with constant angular velocity, Kirchhoff-Love shell modeling of the rotor-blade structure, and full FSI coupling. The analysis cases include the aerodynamics of wind-turbine rotor and tower and the FSI that accounts for the deformation of the rotor blades. The specific wind turbines considered are NREL 5MW, NREL Phase VI and Micon 65/13M, all at full scale, and our analysis for NREL Phase VI and Micon 65/13M includes comparison with the experimental data.