Many of the challenges encountered in computational analysis of wind turbines and turbomachinery are being addressed by the Arbitrary Lagrangian–Eulerian (ALE) and Space–Time (ST) Variational Multiscale (VMS) methods and isogeometric discretization. The computational challenges include turbulent rotational flows, complex geometries, moving boundaries and interfaces, such as the rotor motion, and the fluid–structure interaction (FSI), such as the FSI between the wind turbine blade and the air. The core computational methods are the ALE-VMS and ST-VMS methods. These are supplemented with special methods like the Slip Interface (SI) method and ST Isogeometric Analysis with NURBS basis functions in time. We describe the core and special methods and present, as examples of challenging computations performed, computational analysis of horizontal- and vertical-axis wind turbines and flow-driven string dynamics in pumps.