Advances in numerical relativity since 2005 have led to rapid progress in the modelling of black hole inspirals. Yet an important frontier awaits: the large mass-ratio regime. For example, in the final year before merger, an Extreme Mass-Ratio Inspiral (EMRI) will undergo 10^5 orbits in the strong-field regime. EMRIs may be analysed via black hole perturbation theory, by assuming the small body follows a trajectory on the background spacetime of the large black hole, and that the trajectory is perturbed away from a geodesic of the background by a `self-force'.

In the first half of my talk, I will describe three emerging themes in the self-force programme: (i) comparison of gauge-invariant results from gravitational self-force (GSF) calculations with other methodologies (e.g. Post-Newtonian, EOB and NR); (ii) self-consistent long-term orbital evolutions of EMRIs using GSF calculations; (iii) understanding of qualitatively new phenomena, such as resonances [arXiv:1009.4923], which have practical implications for data analysis strategies.

In the second half of my talk, I will describe recent progress towards the first calculation of GSF on the Kerr spacetime, using a time-domain method.