Convective motions must be responsible for transporting essentially all the thermal energy from the interior of the earth to the surface layers of the planet. This thermal energy is derived from sources such as radioactive decay, cooling of the planet, and from the release of gravitational energy associated with growth and differentiation of the core. While the very presence of plate tectonics on earth is often considered prima facie evidence for at least upper mantle convection, the motion of the lithospheric plates on the surface of the earth also gives an indication of the patterns of convection in the underlying layers of the mantle.Convective motions are difficult to rigorously model in general because of the three dimensional, time dependent, multiple scale, nonlinear nature of the flows involved, and the complex rheology of the matter itself. Thus, while it is relatively easy to construct simplified models for how the Convective motions may be occurring on a global scale, or even detailed models of small‐scale phenomena, a rigorous, global model of the Convective processes in the earth's mantle and core, at the present time as well as throughout its evolution, consistent with the constraints imposed by geophysics, geochemistry, and dynamical modeling, does not exist. This deficiency is the fundamental problem that motivates much of the work on convection reviewed in this paper.