Many properties of planets such as their interior structure and thermal evolution depend on the high-pressure properties of their constituent materials.This paper reviews how crystal structure prediction methodology can help shed light on the transformations materials undergo at the extreme conditions inside planets.The discussion focuses on three areas:(i) the propensity of iron to form compounds with volatile elements at planetary core conditions (important to understand the chemical makeup of Earth’s inner core),(ii) the chemistry of mixtures of planetary ices (relevant for the mantle regions of giant icy planets),and (iii) examples of mantle minerals.In all cases the abilities and current limitations of crystal structure prediction are discussed across a range of example studies.