The immersed boundary method (IBM) has emerged as a powerful and flexible computational framework for simulating flows around complex, moving geometries, circumventing significant mesh-generation burden of body-conformal approaches. Its application to high-Reynolds-number wall-bounded turbulence, however, presents formidable challenges in accurately resolving the thin near-wall region without prohibitive computational cost. This work presents recent advances in overcoming these limitations through the synergistic coupling of IBM with turbulence wall models. However significant challenges arise towards the wall surface quantities, because of the non-smooth distribution of the boundary grids relative to the wall. Spurious oscillations completely pollute the skin friction and the surface pressure, which eventually leads to wrong estimations of the drag and lift forces. The new developments will be presented for reducing these spurious oscillations and improving the estimation of wall surface forces. Then, the embedding of IBM within hybrid RANS-LES frameworks is discussed, highlighting strategies where IBM efficiently handles the geometry while the turbulence model seamlessly transitions from RANS closures in attached boundary layers to LES resolution in separated regions and the free stream. Finally, the application of this combined IBM/wall-model/hybrid turbulence methodology to problems of fluid-structure interaction is explored. This work synthesizes key developments, identifies persistent challenges in accuracy and stability, and underscores the potential of this integrated approach as a transformative tool for the predictive simulation of turbulent flows in complex engineering systems.