Density functional theory (DFT), employing semilocal approximations to describe electron exchange and correlation effects, tremendously advanced the research in the realm of computational catalysis. It allows to calculate atomic and electronic structure details of extended systems like bulk solids, surfaces or nanoparticles with reasonable accuracy at moderate computational cost. However, semilocal approximations suffer from shortcomings such as self-interaction errors (SIEs). This work discusses results obtained using two established and related approaches, namely DFT + U and orbital-dependent hybrid density functionals. Both methods partially alleviate some of the problems incurred by SIEs and are widely used in the computational community. We discuss four case studies involving reducible oxide materials: (i) the oxidative dehydrogenation of methanol at small vanadium oxide clusters supported on the CeO2(111) surface, (ii) the adsorption of Au atoms on the reduced CeO2(111) surface, (iii) stabilities of various terminations of the V2O3(0001) surface, and (iv) the adsorption of water on the Fe3O4(111) surface. Compared with semilocal functionals including DFT + U, we report substantial improvements in band gaps, defect formation energies, as well as activation barriers and emphasize the important role of state-of-the-art experiments for assessing DFT. Limitations of hybrid functionals due to the imposed computational workload and inherent functional approximations are discussed. To overcome these limitations, alternatives in terms of generalized RPA and embedded wavefunction-based methods are suggested.