Abstract: We review some of the most recent developments in classical and quantum mechanical molecular dynamics simulations, in particular as applied to Earth-forming phases at conditions prevalent in the Earth's deep interior. We pay special attention to the modelling of high pressures and temperatures, elucidating the problems associated with both the classical and quantum approaches in view of the empirical potentials required for the former, and the limitations of finite temperature calculations for the latter. We show the current status of such calculations for major phases such as MgSiO₃ perovskite.