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Gravitational wave data analysis of compact binary systems requires the use of matched filtering. This technique cross-correlates the data stream with a certain template that characterizes the gravitational wave signal. Successful parameterestimation thus requires an accurate model of the gravitational wave template. In this talk I will describe a new fast and accurate technique to model the gravitational wave signal from extreme-mass ratio inspirals. Such events consisting of a neutron star or solar mass black hole spiraling into a supermassive black hole are staple sources of the Laser Interferometer Space Antenna. This new model combines the effective-one-body formalism of post-Newtonian theory and black hole perturbation theory leading to accurate waveforms both when the supermassive black hole spins and when it does not.