Superplumes in the lower mantle have been inferred for a long time by the presence of two very large provinces with slow seismic wave velocities. These extensive structures are not expected from numerical and laboratory experiments nor are they found in thermal convection with constant physical properties under high Rayleigh number conditions. Here we summarize our dynamical understanding of superplume structures within the framework of thermal convection. The numerical studies involve both two- and threedimensional models in Cartesian and spherical-shell geometries. The theoretical approach is based on models with increasing complexity, starting with the incompressible Boussinesq model and culminating with the anelastic compressible formulation. We focus here on the (1) depth-dependence of variable viscosity and thermal coefficient of expansion (2) radiative thermal conductivity and (3) both upper- and deep-mantle phase transitions. All these physical factors in thermal convection help to create conditions favorable for the formation of partially-layered convection and large-scale upwelling structures in the lower mantle.