Extracting science from gravitational wave observations requires theoretical modeling, both analytical and numerical. The current state of these models is sufficient for present-day detectors, but next generation detectors bring the promise and challenge of much higher signal-to-noise ratios. This demands we understand the fine details: our modeling errors must be smaller than statistical noise. I'll go into some of the subtle details: (i) The beginnings of our numerical waveforms need to be stitched to analytical approximations; and (ii) The late portion of our numerical waveforms can be modeled as "quasinormal ringing," which must include nonlinearities. Getting both of these right is harder than it sounds!