Most seismic analyses of Earth structure rely on observations of the traveltimes and waveforms of direct seismic waves that travel along ray paths determined by Earth's large-scale velocity structure. These observations permit inversions for radially averaged P wave and S wave velocity profiles as well as three-dimensional (3-D) perturbations. However, smaller-scale velocity or density perturbations cause some fraction of the seismic energy to be scattered in other directions, usually arriving following the main phase as incoherent energy over an extended time interval. This later-arriving wavetrain is termed the coda of the direct phase. Given the number of different scattering events and the complexity of the scattered wavefield, it is generally impossible to resolve individual scatterers. Instead, coda-wave observations are modeled using random media theories that predict the average energy in the scattered waves as a function of scattering angle, given the statistical properties of the velocity and density perturbations. In this way, it is possible to characterize Earth's heterogeneity at much smaller scales than can be imaged using tomography or other methods.The fact that direct seismic waves can be observed in the Earth indicates that this scattering must be relatively weak so that a significant fraction of the seismic energy remains in the primary arrivals. In contrast, scattering on the Moon is proportionally much stronger than in the Earth, preventing the easy observation of direct P and S waves at global distances (at least at the recorded frequencies of the available data) and complicating inversions for lunar structure. In addition to facilitating observations of direct arrivals, weak (as opposed to strong) scattering can also simplify modeling by permitting use of single-scattering theory (i.e., the Born approximation). However, it is now clear that accurate modeling of scattering in the lithosphere, and possibly deeper in the mantle as well, requires calculations based on multiple scattering theories. Fortunately, increased computer power makes these calculations computationally feasible.Although both body waves and surface waves exhibit scattering, the emphasis in this review is on observations and modeling of deep-Earth scattering, 695