Computational flow analysis is now playing a key role in aerospace, energy and transportation technologies, bringing solution in challenging problems such as aerodynamics of parachutes, thermo-fluid analysis of ground vehicles and tires, and fluid–structure interaction (FSI) analysis of wind turbines. The computational challenges include complex geometries, moving boundaries and interfaces, FSI, turbulent flows, rotational flows, and large problem sizes. The Residual-Based Variational Multiscale (RBVMS), ALE-VMS and Space–Time VMS (ST-VMS) methods have been quite successful serving as core methods in addressing the computational challenges. The core methods are supplemented with special methods targeting specific classes of problems, such as the Slip Interface (SI) method, Multi-Domain Method, and the “ST-C” data compression method. We describe the core and special methods. We present, as examples of challenging computations performed with these methods, aerodynamic analysis of a ram-air parachute, thermo-fluid analysis of a freight truck and its rear set of tires, and aerodynamic and FSI analysis of two back-to-back wind turbines in atmospheric boundary layer flow.