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We review our recent results on the implementation of picosecond (ps) X-ray absorption spectroscopy to probe the electronic and geometric structure of centres formed by photoexcitation of solar materials such as TiO2 polymorphs and inorganic Cs-based perovskites. The results show electron localization at Ti defects in TiO2 anatase and rutile and small hole polaron formation in the valence band of CsPbBr3, all within 80 ps. This method is promising for the study of the ultrafast time scales of such processes, especially with the advent of the Swiss X-ray Free Electron Laser (SwissFEL).