Oscillatory shear is a widely used characterization technique for complex fluids but the microstructural changes that produce the material response are not well understood. We apply a recent micromechanical model to soft particle glasses subjected to oscillatory flow. We use particle scale simulations at small, intermediate and large strain amplitudes to determine their microstructure, particle scale mobility, and macroscopic rheology. The macroscopic properties computed from simulations quantitatively agree with experimental measurements on well-characterized microgel suspensions, which validate the model. At the mesoscopic scale, the evolution of the particle pair distribution during a cycle reveals the physical mechanisms responsible for yielding and flow and also leads to quantitative prediction of shear stress. At the local scale, the particles remain trapped inside their surrounding cage below the yield strain and yielding is associated with the onset of large scale rearrangements and shear-induced diffusion. This multiscale analysis thus highlights the distinct microscopic events that make these glasses exhibit a combination of solid-like and liquid-like behavior. (C) 2013 The Society of Rheology. [http://dx.doi.org/10.1122/1.4802631]