The inner core has the intriguing property that seismic waves traveling parallel to the Earth's spin axis arrive earlier than those traveling parallel to the equatorial plane. The travel time is some 6 s faster from pole to pole than across the equator. This difference is not the result of different polar and equatorial radii of the inner core, for it would require the inner core to be elongated at the poles by more than one third of its radius. Rather, this 6-s travel time difference is the result of the inner core's being anisotropic; wave speeds differ for different directions of wave propagation. This anisotropy, discovered only in the last decade, is characterized by cylindrical symmetry about an axis approximately aligned with the Earth's spin axis. The anisotropy is believed to be due to a preferred orientation of anisotropic iron crystals composing the inner core, but the mechanisms responsible for creating such a preferred orientation remain uncertain. With the anisotropy now well established as a basic property of the inner core, its quantification and that temporal variations of its orientation have become a vital tool for probing the structure, composition, and dynamics of the Earth's deep interior.¿ 1997 American Geophysical Union