Reduced-order models of the flow in a plane channel flow are constructed in two regimes: a minimal flow unit in which turbulence is sustained, and a transitional flow linearized about the laminar profile. Proper orthogonal decomposition (POD) of data from a direct numerical simulation of a channel flow in a minimal flow unit is performed in order to examine the coherent structures and their dynamical interactions. Empirical basis functions are obtained both using Fourier modes in the streamwise and spanwise directions, with POD modes in the wall-normal direction, and using 3D (non-Fourier) POD modes that can translate in the streamwise direction (traveling modes). Traveling modes capture more energy than standard Fourier-POD for the same number of modes. In addition, models of a channel flow linearized about a laminar profile are constructed using both POD and balanced POD, an approximation to balanced truncation that is tractable for very large systems. Balanced POD models significantly outperform standard POD, especially at including the effects of actuation.