High computational expense prohibits direct numerical simulation of turbulent flows for time-sensitive applications including real-time prediction and control. To address this, reduced-order modeling techniques reduce system dimensionality while maintaining pertinent dynamics. In this thesis, two such techniques---the Green's function method and fluctuation-dissipation theorem---were employed to compute the linear response function of turbulent plane Couette flow at Reynolds numbers of 5,000 and 10,000. Outputs from these methods were validated in both prediction and control applications. The reduced-order models from Green's function method performed well across Reynolds number and problem type, while the model from fluctuation-dissipation theorem performed poorly due to the non-normality of the underlying system. Spectral analysis of the reduced-order model from the Green's function method suggests a previously-unexplored connection with Hankel-dynamic mode decomposition and shows substantial difference in turbulence closure between the Reynolds numbers considered, challenging conventional universal closure models.