This thesis investigates the photoinduced charge carrier dynamics of TiO2 nanoparticles and CsPbX3 (X = Cl, Br) nanocrystals, by means of ultrafast x-ray absorption spectroscopy (XAS) and transient absorption spectroscopy (TAS). TiO2 is among the most promising transition metal oxides for applications such as photocatalysis and photovoltaics. In the latter, TiO2 has been used over the years in dye-sensitized solar cells (DSSCs) as electron transport material. CsPbX3 belongs to the class of lead halide perovskites and is currently one of the most investigated materials for solar energy applications, due to the high conversion efficiencies and ease of preparation. These materials are commonly used in solar cells with an all-solid-state DSSC architecture as light absorbers. Solar energy conversion is governed by the generation of charge carriers, their subsequent evolution as excitons or free charge carriers, and eventually their localization. Ultrafast spectroscopy can gain insights into the evolution of charge carriers by following their dynamics in real time. For this reason, ultrafast XAS was the main technique used in this work, as it combines elemental and structural sensitivity to study the fate of charge carriers and their evolution under operating conditions. The early stages of electron localization in TiO2 anatase nanoparticles upon photoexcitation at 3.5 eV, are investigated by fs-XAS at the Ti K-edge using the synchrotron slicing technique. The results show that localization of electrons at Ti atoms occurs in < 300 fs, forming Ti3+ centres, in or near the unit cell where the electron is excited. Moreover, electron localization is due to its trapping at pentacoordinated sites, mostly present in the surface shell region. Similar conclusions are drawn for another polymorph of TiO2, rutile, from ps-XAS at the Ti K-edge. Here electrons are trapped next to oxygen vacancies at 100 ps after photoexcitation. Electrons in rutile though, show a weaker tendency to localization than in anatase and this could explain the differences in photocatalytic performances between these two polymorphs. In the second part of this thesis, the ultrafast charge carrier dynamics of CsPb(ClBr)3 nanocrystals is investigated using fs-TAS in the visible region (~1.8-3.1 eV) upon photoexcitation at 3.1 eV. This material represents an ideal system to study the ultrafast physics of lead halide perovskite in general, because ultrafast TA studies suggest that the charge carrier dynamics are similar to the organic-inorganic materials but do not suffer from the same stability issues. Here, the ultrafast transition from free charge carriers to excitons is observed in a fluence dependent study, which sheds light on the interpretation of a long lived spectral feature rising from a transient electroabsorption effect. Finally, the charge carrier dynamics of CsPbX3 (X = Cl, Br) is investigated using ps-XAS at the Br K-edge, the Pb L3-edge and Cs L2-edge upon photoexcitation at 3.5 eV. The Br K-edge transients at 100 ps delay show evidence for a full electron charge being withdrawn from the Br atoms, i.e. the hole is localized due to formation of a small polaron. The transients at the Pb L3-edge point to the opposite, i.e. the electrons are fully delocalized as conduction band electrons and there is no hint of trapping. Lastly, the Cs L2-edge shows no transient signal, in agreement with predictions based on the partial density of states in the material.