Earth's surface is constantly warped up and down by the convecting mantle. Here we derive geodynamic rules for this so-called dynamic topography by employing high-resolution numerical models of global mantle convection. We define four types of dynamic topography history that are primarily controlled by the ever-changing pattern of Earth's subduction zones. Our models provide a predictive quantitative framework linking mantle convection with plate tectonics and sedimentary basin evolution.