Compact remnants on orbits with peri-apses close to the Schwarzschild radius of a massive black hole (MBH) lose orbital energy by emitting gravitational waves (GWs) and spiral in. Scattering with other stars allows successful inspiral of such extreme mass ratio inspiral sources (EMRIs) only within small distances, a < few times 0.01 pc from the MBH. The event rate of EMRIs is therefore dominated by the stellar dynamics and content in the inner few times 0.01 pc. I discuss the relevant dynamical aspects and resulting estimated event rates of EMRIs. Subjects considered include the loss-cone treatment of inspiral sources; mass segregation; resonant relaxation; and alternative routes to EMRI formation such as tidal binary disruptions, stellar formation in disks and tidal capture of massive main sequence stars. The EMRI event rate is estimated to be of order few times 102/Gyr per MBH, giving excellent prospects for observation by LISA.