Measurements of magnetic and gravitational fields in planetary science are usually combined with numerical models to unveil the interior structures, dynamics, and history of planets. However, these models are highly dependent on poorly constrained physical properties of planets' interiors, that can be only understood through experimental and theoretical developments of material science at extreme conditions. Furthering the limits of experimental and theoretical pressures and temperatures for materials such as hydrogen, helium, ammonia, water, methane, iron, silicates (just to name a few) will help to better our understanding of the history and evolution of giant and terrestrial planets. In this presentation I will talk about numerical models of planetary interiors, showing how transport properties of materials at extreme conditions contribute to the development and success (or failure) of these models.