We review recent progress in studying structural properties of liquids using X-ray absorption spectroscopy coupled with the Paris-Edinburgh press at third-generation synchrotron facilities. This experimental method allows for detecting subtle changes in atomic arrangements of melts over a wide pressure-temperature range. It has been also employed to monitor variations of the local coordination environment of diluted species contained in glasses, liquids and crystalline phases as a function of the pressure and temperature. Such information is of great importance for gaining deeper insights into the physico-chemical properties of liquids at extreme condition, including the understanding of such phenomena as liquid-liquid phase transitions, viscosity drops and various transport properties of geological melts. Here, we describe the experimental approach and discuss its potential in structural characterization on selected scientific highlights. Finally, the current ongoing instrumental developments and future scientific opportunities are discussed.