Accurate prediction of high-Reynolds-number wall-bounded 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 gradient, flow separation, and mean three-dimensionality. 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 the 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 work, we focus on two aspects of wall models, (i) development and implementation of new/existing wall models, and (ii) application and comparison of different wall models in various nonequilibrium turbulent boundary layers. In the first part, we develop a novel spectral formulation for the ODE equilibrium wall model, showing its superior efficiency over the traditional approach. Furthermore, we extend the integral nonequilibrium wall model to an \textit{unstructured-grid} LES solver. In the second part, we explore three wall models with varying degrees of computational complexity and physical fidelity, to assess their performance in two controlled but reasonably realistic 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 that there still exists the need to adapt the existing wall models to different flow physics by modifying their underlying formulation or assumptions. Finally, a physic-based decomposition of skin friction, that shows separable contributions from various physical processes in the flow, is employed to explain the differing mechanisms of success/failure of wall models in different flows.