Riemannian spaces are described by non-orthogonal curvilinear coordinates. We generalize one-way wavefield extrapolation to semi-orthogonal Riemannian coordinate systems, which include, but are not limited to, ray coordinate systems. We obtain one-way wavefield extrapolation methods which are not dip-limited, and which can even be used to image overturning waves. Ray coordinate systems can be initiated either from point sources, or from plane waves incident at various angles. Since wavefield propagation happens mostly along the extrapolation direction, we can use cheap finite-difference or mixed-domain extrapolators to achieve high angle accuracy. The main applications of our method include imaging of steeply dipping or overturning reflections.