While wall-modeled large-eddy simulation (WMLES) has become an indispensable numerical tool for scale-resolving simulations and shows its superiority compared to other computational fluid dynamics tools in high Reynolds-number wall-bounded turbulent flows, there are still several challenges remaining to be resolved. The first challenge is the assessment of wall models' capabilities in nonequilibrium turbulent boundary layers with pressure gradient and mean-flow three-dimensionality. WMLES of a pressure-driven three-dimensional turbulent boundary layer (3DTBL) developing on the floor of a bent square duct is conducted to investigate the predictive capabilities of three widely used wall models, namely, a simple equilibrium stress model, an integral nonequilibrium model, and a PDE nonequilibrium model. While the wall-stress magnitudes predicted by the three wall models are comparable, the PDE nonequilibrium wall model produces a substantially more accurate prediction of the wall-stress direction. The wall-stress direction from the wall models is shown to have separable contributions from the equilibrium stress part and the integrated nonequilibrium effects, where how the latter is modeled differs among the wall models. Another challenge is to demonstrate the invariance of the WMLES results with respect to the mesh resolution. It is proposed that the extent of the wall-modeled region controls the convergence trajectory. Specifically, the onset of convergence is expected to occur at coarser grid resolutions when larger extents of the wall-modeled region are employed. The proposition is examined in both channel flow and a 3DTBL. The obtained results provide compelling evidence supporting the idea. Lastly, why dynamic model in LES works is still not well understood. In the present work, it is postulated that the principal directions of the resolved rate-of-strain tensor play an important role in the dynamic model. Specifically, it is found that minimization of the GIE along only the three principal directions, in lieu of its nine components in its original formulation, produces equally comparable results as the original model, suggesting that there might be dynamically more important directions for modeling the subgrid dynamics.