The chaotic nature of turbulent flows results in a broad spectrum of flow scales, including at the same time very large and very small eddies. For this reason, the direct numerical simulation of turbulent flows is often unaffordable, and one resorts to large eddy simulation (LES): only the large eddies are resolved, while the effect of the small eddies is modeled. Although this method leads to a significant reduction of the computational cost of such simulations, problems still arise in the case of turbulent wall-bounded flows. In this case, the largest eddies of the flow are still locally very small in the vicinity of the wall (the ``inner wall layer’’), and the cost reduction of LES is only marginal. In this thesis, we explore a family of models that further reduce the computational cost of the LES of wall-bounded flows: wall shear stress models. These models aim at providing a model for the inner wall layer, to alleviate the need to resolve the largest-yet tiny—eddies of this flow region. Such models have existed for some time in the literature; yet, their behavior is still poorly understood. We here provide a study of these models in cases of increasing complexity. First, a study in channel flow, hence with the wall layer at equilibrium in space and in time, is carried out. The impact of the various parameters of the simulation is analyzed. Second, two further cases are analyzed, wherein the flow is out of equilibrium. One is only a mild departure from equilibrium, while, in the other, the whole wall layer is strongly altered.