Recent diamond-anvil cell experiments are providing windows of unprecedented clarity on the interiors of the Earth, other planets, and their moons from high P-T studies of the materials that comprise these bodies. With recent advances in techniques, the component minerals can be examined with a growing array of in situ methods over an expanding range of conditions that extend to hundreds of gigaspascals in pressure and thousands of degrees in temperature. Such investigations reveal that major, if not profound, changes in physical and chemical properties of these materials occur with depth. This information is crucial for understanding the materials basis of regional to global structure and processes documented by a wealth of recent observational and geophysical data. This paper reviews selected recent studies of major planet-forming minerals, focusing on key examples that illustrate different microscopic origins of macroscopic behaviour. This comparative mineralogical approach provides insight into phenomena occurring over a wide range of length scales. For terrestrial planets, the high-pressure behaviour of representative silicates, oxides and sulphides is examined. This includes the silicate perovskite assemblages that form the bulk of the Earth's lower mantle, for which a number of new findings concerning effects of non-stoichiometry and defect properties, pressure-induced electronic and magnetic transitions, and rheology have been obtained. High P-T studies of Fe-Ni alloys, together with various light elements, provide constraints on the composition, structure and dynamics of terrestrial planet cores. Water is a key component of many planetary bodies; as ice it undergoes numerous high-pressure transformations and as a volatile component it is involved in potentially important high P-T mineral reactions and is incorporated in dense mineral phases. Striking behaviour is observed in other molecular systems, including CO2 and CH4 and their mixtures with H2O; these form new phases, some relevant at the relatively modest conditions of deep marine sediments, others at the extreme states found in the deepest planetary interiors. Additional high P-T interactions between rare gases and ices and silicates are also documented. For the large planets, the most abundant ‘mineral’ is hydrogen, which has been shown to undergo novel mineral/gas reactions, possibly in cloud decks deep within the dense atmospheres of these bodies.