Novel techniques and the experimental station for experiments on condensed matter under extreme conditions that have been developed at the BM29 beamline of the European Synchrotron Radiation Facility (ESRF) are described. The experimental setup includes facilities to collect high-quality extended X-ray absorption fine structure (EXAFS) spectra, to perform controlled temperature scans while monitoring the sample absorption for the direct detection of phase transitions, and to collect high-resolution energy-scanning X-ray diffraction (ESXD) data, with recent enhancements through the installation of a two-channel collimator detector system. Facilities for X-ray absorption temperature scans, introduced five years ago, are now exploited for a wide variety of purposes. A method for the measurement of the nucleation rate in undercooled liquids has been proposed recently. All these advances in the experimental setup and techniques, combined with a simple but rigorous X-ray absorption fine structure (XAFS) data analysis scheme for disordered matter, have contributed to make feasible challenging experiments on undercooled liquid matter that were not even conceivable only a few years ago. An example of the application of these methods to undercooled liquid indium (In) is presented.