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Extreme mass ratio inspirals (EMRIs) show a strong separation of timescales,with the time characterizing inspiral, $T_{\rm i}$, much longer than any time$T_{\rm o}$ characterizing orbital motions. The ratio of these timescales(which is essentially an EMRI's mass ratio) can be regarded as a parameter thatcontrols a perturbative expansion. Here we describe the value and limitationsof an "adiabatic" description of these binaries, which uses only the leadingterms arising from such a two-timescale expansion. An adiabatic approach breaksdown when orbits evolve through resonances, with important dynamical andobservational consequences. We describe the shortfalls of an approach that onlyincludes the adiabatic contributions to EMRI evolution, and outline what mustbe done to evolve these systems through resonance and to improve our ability tomodel EMRI systems more generally.

Adiabatic and post-adiabatic approaches to extreme mass ratio inspiral