The 1980 IAU nutation series includes effects of the Earth's non-rigidity. Certain simplifying assumptions were made in the model, including that the Earth is elastic and hydrostatically pre-stressed. The rationale was that geophysicists didn't understand the Earth well enough to justify a relaxation of those assumptions, and that the nutation observations were not accurate enough to detect the difference, anyway. Geophysicists are still not able to construct a more accurate model that is independent of the nutation observations, themselves. But, the observations have improved enormously. Recent results obtained from VLBI data show discrepancies with the IAU model of close to 2 milliseconds of arc: many times the observational uncertainty. Thus, the nutation observations are beginning to tell us things about the Earth that cannot presently be inferred as accurately from other techniques. I will discuss some of these possible geophysical applications. Among them are the shape and internal structure of the core, and the Earth's anelasticity.