Of the potential sources of gravitational waves, two of the most fascinating candidates are compact-object binary systems and cosmic strings. Binary systems typically involve a pair of neutron stars or black holes inspiralling and coalescing to produce a single remnant. On the other hand, cosmic strings are a generic feature predicted by a large number of cosmological models and fundamental physics; like binary systems their existence is expected to generate large amounts of gravitational radiation. Although these two phenomena are quite distinct in their origins and physical features, both can be modelled using closely related techniques. This talk presents a novel approach to both problems which combines new numerical and analytical methods and yields geometrical insight into the contributions to self-interaction from curved geometry (back-scattering) and trapping of null geodesics.