In this chapter we summarize a recently proposed immersogeometric method for the simulation of incompressible flow around geometrically complex objects. The method immerses the objects into unfitted tetrahedral finite elements meshes and weakly enforces Dirichlet boundary conditions on the surfaces of the objects. Adaptively refined quadrature rules are used to faithfully capture the flow domain geometry in the discrete problem without modifying the unfitted finite element mesh. A variational multiscale formulation which provides accuracy and robustness in both laminar and turbulent flow conditions is employed. We assess the accuracy of the method by analyzing the flow around an immersed sphere for a wide range of Reynolds numbers. We show that flow quantities of interest are in very good agreement with reference values obtained from standard boundary-fitted approaches. Our results also show that the faithful representation of the geometry in intersected elements is critical for accurate flow analysis. We demonstrate the potential of our proposed method for high-fidelity industrial scale simulations by performing an aerodynamic analysis of a full-scale agricultural tractor.