The recent direct detection of gravitational waves has brought the promise of a novel source of information about the Universe. Gravitational waves from compact binaries primarily depend on the masses of the binary components, but the binary components' spins play an important role too. Interactions between the spins and the orbital angular momentum of the binary give rise to modulations in the amplitude and phase of the wave. These spin-induced precessional modulations are hard to model and measure, yet they carry invaluable information about the binary and the environment that created it. In this talk I will describe efforts to analytically model these spin-precessional modulations accurately and efficiently. I will also describe how this can be used to compute gravitational waveforms that describe the entire evolution of a compact binary as seen by LIGO, including the violent merger and eventual ringdown.