Active research is ongoing that investigates the properties of matter under extreme pressure. Such condensed matter is found inside planets at millions of atmospheres and thousands of degrees kelvin. Extreme pressures coupled with high temperatures can also be used to synthesize new materials with advanced properties. This Primer outlines how a new generation of X-ray user facilities are essential to measure the microscopic properties of matter under such conditions, with scattering and absorption methods being the most used. This article explains how extreme thermodynamic states can be achieved, either by dynamic laser shock or static diamond anvil cell compression, and how the high-brilliance X-ray beams produced at synchrotrons and hard X-ray free electron lasers can be utilized to investigate very dense matter with a high level of detail and accuracy at the microscopic level. Cross-fertilization between the static and dynamic communities has led to new approaches, bridging timescales and opening new perspectives to understanding dynamic processes at high pressure. To illustrate this, two examples are highlighted: iron and carbon. Reproducibility issues and some limitations are discussed, ending with an evaluation of future opportunities.
