Unsteady Couette granular flows are investigated both theoretically and by the means of the discrete element method (DEM). Theoretical formulation of the problem is based on the kinetic theory for smooth, nearly elastic particles. The resulting boundary value problem is solved numerically for two particular types of flows: (a) transient Couette flows, in which the wall velocity instantaneously changes from one constant value to another, and (b) cyclic Couette flows, in which the wall velocity is a harmonic function of time. The behavior of granular fluids in these flows is found to critically depend on the ratios of time scales that characterize the rate of change of the wall velocity and processes of momentum diffusion and energy relaxation. The limiting case in which the momentum diffusion time scale is much smaller than the energy relaxation time scale is also analyzed analytically by perturbation methods. In this limit granular materials behave as nearly incompressible non-Newtonian fluids. Hence, under appropriate conditions, which correspond to small Mach numbers, mathematical analysis of rapid granular flows can be tremendously simplified. For both transient and cyclic Couette flows, predictions of the kinetic theory for disks are found to be in a very good agreement with the corresponding DEM simulations at all time scales as long as the coefficient of restitution is close to unity. However, as the coefficient of restitution decreases, the agreement deteriorates due to a gradual breakdown of assumptions used in the development of the nearly elastic kinetic theory.