<p>Fluorite-structured materials such as cerium dioxide (ceria or CeO₂), zirconium dioxide (zirconia or ZrO₂), uranium dioxide (urania or UO₂), and thorium dioxide (thoria or ThO₂) are technologically important for solid oxide fuel cells (SOFC) and nuclear fuels. As such, they have an important role in the future energy mix, and their properties under a range of pressure and temperature conditions need to be understood. There is significant research effort on the material properties of classic oxide systems, both from an experimental and theoretical perspective, aiming to improve these systems using doping or external parameters such as strain. Here, we briefly review cation and oxygen diffusion in fluorite-structured materials. Emphasis is given on the impact on the diffusion of external parameters such as strain.</p>