The three-dimensional shear-driven cavity flow is numerically investigated at Reynolds numbers of 5000 and 10000. This investigation focuses on the unsteadiness and turbulent characteristics of the flow. At the moderate Reynolds number (Re = 5000) where the cavity flow is fully laminar, a direct numerical simulation (DNS) is used whereas large-eddy simulation (LES) methodology is adopted to predict the cavity flow at the higher Reynolds number (Re = 10000). Establishing a suitable form for the subgrid scale (SGS) turbulence model in this complex flow is guided by the DNS results at Re = 5000. Additionally, the SGS model is verified against DNS results at Re = 7500 where the cavity flow is known through experimentation to be locally transitional. The LES results verify the published experimental evidence as well as uncover new flow features within the cavity.