Consider a stellar-mass black hole (mass $\sim 10$ solar masses) in a
 close orbit around a supermassive black hole (mass $\sim 10^6$ solar
 masses).  In this talk I'll discuss the challenge of trying to model
 the orbital dynamics and gravitational-wave (GW) emission of such an
 "EMRI" system as it evolves under the influence of the gravitational
 radiation-reaction "self-force".  Because of the highly asymmetric
 mass ratio the orbital-decay timescale is much longer than the orbital
 period, so a direct "numerical relativity" solution of the Einstein
 equations would be both impractically expensive and insufficiently
 accurate.  Instead, we can use methods based on black hole perturbation
 theory, treating the small black hole as a perturbation of a background
 (Schwarzschild or Kerr) spacetime.  I'll outline some of the analytical
 and computational challenges of these analyses, describe recent
 progress in surmounting these challenges, and discuss EMRI systems
 as potential GW sources for the proposed eLISA/NGO space-based GW
 observatory.