Although the idea of an X-ray absorption spectrometer in dispersive geometry was initially conceived for the study of transient phenomena, the instrument at the European Synchrotron Radiation facility has been increasingly exploited for studies at extreme conditions of pressure using diamond anvil cells. The main results of investigations at high pressure obtained at beamline ID24 are reviewed. These concern not only fundamental topics, such as the local and the electronic structure as well as the magnetic properties of matter, but also geological relevant questions such as the behaviour of Fe in the main components of the Earth's interior.