CuO nanoparticles (NPs) and Cu₂O/CuO and CuO/TiO₂ nanocomposites (NCs) have been synthesized by using a modified co-precipitation method with three different schemes of synthesis. The crystal structures and morphologies of the samples have been investigated using synchrotron X-ray diffraction and transmission electron microscopy, respectively. The detailed local electronic structures of the NPs and NCs have been determined using X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) spectroscopy. O K-, Cu K- and Cu L-edge XANES spectra revealed a dominant +2 valence state of Cu in the case of the CuO NPs and CuO/TiO₂ NCs, although Cu⁺¹ was dominant in the Cu₂O/CuO NCs. A comparison of the local atomic structure around the Cu sites revealed shorter Cu–O bond distances in the as-synthesized samples with respect to the bulk CuO or Cu₂O. The Ti K-edge EXAFS fittings for the CuO/TiO₂ NCs revealed that the local anatase TiO₂ phase was formed, with a Ti–O bond distance of 1.98 Å. We further demonstrated that the CuO NPs, and Cu₂O/CuO and CuO/TiO₂ NCs can serve as effective photocatalysts towards the degradation of two novel water pollutants, (i) methyl orange (MO) and (ii) potassium dichromate (PD), under visible light irradiation. It was found that the Cu₂O/CuO NCs exhibit a higher photocatalytic activity towards the degradation of MO and PD than the CuO NPs or CuO/TiO₂ NCs. The mechanism of the photodegradation of MO and PD is also discussed in terms of possible chemical reactions, along with the electronic structure and surface properties of the samples.