Hotspots are associated with long-wavelength geoid highs, an association that is even stronger when the geoid highs associated with subduction zones are removed. We quantify these associations by expanding the hotspot distribution in spherical harmonics and calculating correlation coefficients as a function of harmonic degree. The hotspot distribution spectrum is nearly white, except for peaks at degrees 2 and 6. It is correlated positively with the slab residual geoid for degrees 2--6, with low seismic velocity in the lower mantle at degree 2, and with low seismic velocity in the upper mantle at degree 6. We test fluid mechanical models for hotspots, including lithospheric delamination and hot plumes, by calculating their predicted dynamic geoid responses and comparing them to the observations. These models include the effects of temperature dependent rheology. Our preferred hotspot model, based on observations of the geoid and seismic tomography, has plumes preferentially occurring in regions of large-scale background temperature highs in a mantle which has a substantial viscosity increase with depth, although other models are possible. Alternatively, strong plumes in the lower mantle may neck down and attenuate in the upper mantle due to changes in plume viscosity. The major low-density anomalies causing the geoid highs associated with plumes appear to be in the lower mantle. We hypothesize that cold lower mantle underlying the complementary geoid lows is due to deeply subducted oceanic lithosphere and that hotspot plumes tend to be excluded from these cold regions of the mantle. ¿ Americal Geophysical Union 1988