The propagation of high-frequency seismic waves through inhomogeneous media can often be described well by asymptotic ray theory. Nevertheless, situations in which ray theory breaks down are widespread and of interest: rays may be focused at caustics causing amplitude singularities; wavefronts may contain amplitude discontinuities causing diffracted signals, e.g. at critical points or shadows; signals may be scattered by inhomogeneities causing low-frequency reflections; and rays may couple due to rapid variations in the ray solutions. In this paper, we concentrate on extensions of ray theory that solve the last two problems - scattering and coupling between ray solutions due to inhomogeneities in the model and ray solution.