Mantle convection induces dynamic topography, the lithosphere's surface deflections driven by the vertical stresses from sublithospheric mantle convection. Dynamic topography has important influences on a range of geophysical and geological observations. Here, we studied controls on the Earth's dynamic topography through 3-D spherical models of mantle convection, which use reconstructed past 410 Myr global plate motion history as time-dependent surface mechanical boundary condition. The numerical model assumes the extended-Boussinesq approximation and includes strongly depth- and temperature-dependent viscosity and phase changes in the mantle. Our results show that removing the chemical layer above the core-mantle boundary (CMB) and including depth-dependent thermal expansivity have both a limited influence on the predicted present-day dynamic topography. Considering phase transitions in our models increases the predicted amplitude of dynamic topography, which is mainly influenced by the 410 km exothermic phase transition. The predicted dynamic topography is very sensitive to shallow temperature-induced lateral viscosity variations (LVVs) and Rayleigh number. The preservation of LVVs significantly increases the negative dynamic topography at subduction zones. A decrease (or increase) of Rayleigh number increases (or decreases) the predicted present-day dynamic topography considerably. The dynamic topography predicted from the model considering LVVs and with a Rayleigh number of 6 x 10(8) is most compatible with residual topographymodels. This Rayleigh number is consistent with the convective vigor of the Earth as supported by generating more realistic lower mantle structure, slab sinking rate and surface and CMB heat fluxes. The evolution of the surface heat flux pattern is similar to the long-term eustatic sea level change. Before the formation of Pangea, large negative dynamic topography formed between the plate convergence region of Gondwana and Laurussia. The predicted dynamic topography similar to that of present-day has already emerged by about 262 Ma. Powers for degrees 1-3 dynamic topography at 337 and 104 Ma which correspond to times of higher plate velocities and higher surface heat fluxes are larger.