The history of the discovery of the earth's liquid core and its role in geophysics is briefly reviewed. Among the core's still undetermined properties is the extent to which its density gradient departs from an adiabat, as characterized by the Brunt-Vaisala frequency. Since this parameter must affect the eigenfrequencies of the hitherto unobserved inertia-gravity wave segment of the earth's normal mode spectrum, considerable effort has gone into theoretical studies of these core oscillations over the past decade. We relate these studies to those of internal gravity and Rossby waves in oceanography. The deployment of sensitive gravimeters with long-term recording capability is now begining to yield data in which core modes may already have been observed.