Abstract Recent seismic inferences of the topography on the core-mantle boundary (CMB) constitute a new and potentially important constraint on the dynamics of the thermal convective circulation in the Earth's mantle. We employ viscous flow models for the mantle to predict the flow-induced deflections of the CMB that are expected on the basis of seismic tomographic inferences of internal mantle density heterogeneity. The good agreement between our theoretical predictions and the seismically inferred CMB deflections of Morelli and Dziewonski (1987) suggests that the latter may indeed be good approximations to the dynamically induced CMB topography. The amplitude of the seismically inferred CMB topography may be construed to provide a direct constraint on the temperature derivative of seismic P-wave velocity in the lower mantle and we determine a value for this parameter, in the course of fitting the data, that differs significantly from the value determined by laboratory measurements as appropriate for upper-mantle phases. The seismically observed topography on the CMB is also shown to provide evidence favouring the whole-mantle convection hypothesis and in this connection we argue that deep penetration of subducted lithospheric slabs into the lower mantle is likely to be responsible for controlling many of the features of this topography.