More than 20 years after their discovery, plates and hotspots are still awaiting a consistent dynamic model. Both imply large viscosity variations in the mantle. Sustained efforts have been targeted on modeling (on computer as well as in the laboratory) convection in fluids with temperature- and pressure-dependent viscosity. The main results of these studies are reviewed and summarized in a few simple rules. Several properties of plates, such as ridge-push or heat-flow distribution, are well accounted for by convection models with temperature-dependent viscosity. However, the process of subduction is not properly explained by these models. One of the simple rules deduced from the study of convection and temperature-dependent viscosity states that the viscosity drop across the lower boundary layer adjusts to a low value (less than 10). This contrasts strongly with the viscosity variations required by current hotspot formation models, which are typically 100 times larger. It is suggested that this paradox can be solved if subduction is properly included in the convection models.