Non-colloidal suspensions of spheres undergoing oscillatory shearing flows demonstrate a range of unique, and even surprising, behaviors. Examples from rheological experiments include the existence of a non-monotonic dependence of the complex viscosity upon the strain amplitude and the observation of two distinct scales for the development of the rheology in time. Simulations of the oscillating suspensions predict the non-monotonic relationship between strain amplitude and the steady value of the complex viscosity while providing insights into the underlying microstructure that generates the macroscopic rheology observed in the experiments. Furthermore, the oscillatory rheology is related to the more general dynamics of suspensions within more complicated flows.