We conduct a detailed investigation of defects in two representative amorphous oxides: amorphous Al2O3 (am-Al2O3) and TiO2 (am-TiO2), by combining ab initio molecular dynamics (MD) simulations and hybrid functional calculations. Our results indicate that oxygen vacancies and interstitials occur neither in am-Al2O3 nor in am-TiO2 due to structural rearrangements which assimilate the defect structure, and that the injection of extra holes can lead to the formation of O-O peroxy linkages. In am-Al2O3, hydrogen is found to be amphoteric. Based on localized Wannier functions, we identify the nominal charge state and the composition of the defect core units related to C and N impurities in am-Al2O3, which are found to depend on the total charge set in the simulation cell. Through the adopted electron counting rule, we assess that carbon and nitrogen impurities are only found in neutral and in singly positive charge states, respectively, indicating that none of them gives charge transition levels in am-Al2O3. In addition, those defect core units are shown to incorporate a varying number of oxygen atoms, by which their formation energy is dependent on the oxygen chemical potential. In addition, we propose an exchange mechanism for hole transport in am-TiO2 that relies on the simultaneous breaking and forming of O-O peroxy linkages that share one O atom. Through the use of nudged-elastic-band calculations, a hopping path as long as 1.2 nm with barriers of 0.3-0.5 eV is demonstrated, suggesting that hole diffusion through O-O peroxy linkages is viable in am-TiO2. In this work, we also determine the band alignment between various semiconductors and liquid water by combining MD simulations of atomistic interface models, electronic-structure calculations at the hybrid-functional and GW levels, and a computational standard hydrogen electrode (SHE). Our study comprises GaAs, GaP, GaN, CdS, ZnO, SnO2, rutile and anatase TiO2. For each semiconductor, we generate atomistic interface models with liquid water at the pH corresponding to the point of zero charge. The MD simulations are started from initial configurations, in which the water molecules are either molecularly (m) or dissociatively (d) adsorbed on the semiconductor surface. The calculated band offsets are found to be strongly influenced by the adsorption mode at the semiconductor-water interface, leading to differences larger than 1 eV between m and d models of the same semiconductor. We then assess the accuracy of various ab initio electronic-structure schemes in determining the band alignment. In the last part, we try to evaluate photocatalysts for water-splitting by considering the surface coverage and the energy alignment. We determine surface concentrations of water molecules, protons, and hydroxyl ions adsorbed at the semiconductor-water interfaces mentioned above as a function of pH. This is achieved through the calculation of the acidity constants at the surface sites, which are derived from ab initio MD simulations and a grand-canonical formulation of adsorbates. It is finally shown how the potential of a semiconductor material as photocatalysts for water splitting can be inferred by combining the nature of the surface coverage and the alignment of the band edges to the relevant redox levels.