In megabar shock waves, materials compress and undergo a phase transition to a dense charged-particle system that is dominated by strong correlations and quantum effects. This complex state, known as warm dense matter, exists in planetary interiors and many laboratory experiments (for example, during high-power laser interactions with solids or the compression phase of inertial confinement fusion implosions). Here, we apply record peak brightness X-rays at the Linac Coherent Light Source to resolve ionic interactions at atomic (ångström) scale lengths and to determine their physical properties. Our in situ measurements characterize the compressed lattice and resolve the transition to warm dense matter, demonstrating that short-range repulsion between ions must be accounted for to obtain accurate structure factor and equation of state data. In addition, the unique properties of the X-ray laser provide plasmon spectra that yield the temperature and density with unprecedented precision at micrometre-scale resolution in dynamic compression experiments.