Abstract. Ab initio simulations play an increasingly important role in the studies of deep planetary interiors. Here we review the current state of this field, concentrating on studies of the materials of the Earth's deep interior (MgO--SiO 2 --FeO--Al 2 O 3 , Fe--Si--S--O) and of the interiors of giant planets (H--He system, H 2 O--CH 4 --NH 3 system). In particular, novel phases and phase diagrams, insights into structural and electronic phase transitions, melting curves, thermoelasticity and the effects of impurities on physical properties of planet-forming materials are discussed.