Accurate prediction of high-Reynolds-number turbulent flows is essential for the understanding and flow control of many engineering applications such as aircraft, turbomachinery, and marine vehicles. Additionally, most practical flows exhibit nonequilibrium effects such as pressure gradients and flow separation. However, the direct numerical simulation (DNS) of high-Reynolds-number wall-bounded turbulent flows is not feasible owing to the prohibitive computational cost of resolving small-scale eddies near the wall. Wall-modeled large-eddy simulation (WMLES) presents an affordable predictive alternative to the DNS via approximate modeling of flow physics near the wall (through a wall model) while resolving the outer (larger) scales directly on the computational grid. In this talk, we will explore three wall models with varying degrees of computational complexity and physical fidelity, to assess their performance in two controlled nonequilibrium flows over a flat plate. The first flow features a turbulent boundary layer undergoing a series of complex pressure gradient effects, while the second exhibits turbulent flow separation induced by suction and blowing. While in the latter case, the more complex model clearly produces a superior prediction of the wall shear stress, the same is not necessarily true in the former case, highlighting the importance of adapting the wall models to different flow physics. We will show how differing mechanisms within wall models lead to the observed results.