All the rocky planets in our solar system, including the Earth, initially formed much hotter than their surroundings and have since been cooling to space for billions of years. The resulting heat released from planetary interiors powers convective flow in the mantle. The mantle is often the most voluminous and/or stiffest part of a planet and therefore acts as the bottleneck for heat transport, thus dictating the rate at which a planet cools. Mantle flow drives geological activity that modifies planetary surfaces through processes such as volcanism, orogenesis, and rifting. On Earth, the major convective currents in the mantle are identified as hot upwellings such as mantle plumes, cold sinking slabs, and the motion of tectonic plates at the surface. On other terrestrial planets in our solar system, mantle flow is mostly concealed beneath a rocky surface that remains stagnant for relatively long periods. Even though such planetary surfaces do not participate in convective circulation, they deform in response to the underlying mantle currents, forming geological features such as coronae, volcanic lava flows, and wrinkle ridges. Moreover, the exchange of material between the interior and surface, for example through melting and volcanism, is a consequence of mantle circulation and continuously modifies the composition of the mantle and the overlying crust. Mantle convection governs the geological activity and the thermal and chemical evolution of terrestrial planets and understanding the physical processes of convection helps us reconstruct histories of planets over billions of years after their formation.