Motivated by the search for new backgrounds with solvable string theories, the talk classifies the D-brane geometries leading to integrable geodesics. This analysis gives severe restrictions on the potential candidates for integrable string theories. It is demonstrated that the Hamilton-Jacobi equation for massless geodesics can only separate in elliptic or spherical coordinates, all known integrable backgrounds are covered by this separation, and new examples are constructed. The Killing and Killing-Yano tensors associated with such separation and their transformations under string dualities are also discussed.