Strong electronic correlations have been in the focus of solid state research for quite some time. Many interesting phenomena such as the Mott metal-to-insulator transition, superconductivity (both conventional and unconventional) or heavy-fermion systems can only be explained when taking correlation effects into account. In this regard there has always been the hope that applications exploiting these correlation effects will one day replace or enhance current technologies. One of the most promising group of materials with respect to applicability are transition metal oxides which are at the center of this thesis. In order to be able to describe the involved physics we will, in the first part of this thesis, construct the bridge from the many-body problem in first quantization to the Greens function formalism and subsequently Feynman diagrammatic. With this formalism we are able to introduce the state-of-the-art density functional theory (DFT) + dynamical mean-field theory (DMFT) approach both from a physical point of view and, more importantly, diagrammatically. This technique allows for an accurate description of genuine (local) correlation effects. However due to the underlying mean-field approach in the spatial domain non-local effects are out of its reach. These non-local correlations play an essential role in two-dimensional structures (e.g. ultra-thin films) or near phase transitions. For this reason many theories and techniques have been developed which extend DMFT to capture both the local correlations of DMFT and non-local correlations beyond. The dynamical vertex approximation (DA) represents one of the diagrammatic extensions of DMFT and will be our main focus point in this thesis. With it, in the second part of this thesis, we will further investigate a common testbed material used in electronic structure calculations, namely strontium vanadate (SrVO 3 ). More specifically we will study the effects of temperature and non-local interactions in bulk SrVO 3 as well as the effects of the previously mentioned reduced dimensionality. The latter is based on recent findings that two-layered SrVO 3 on a substrate of strontium titanate (SrTiO 3 ) could be potentially used as a so-called ‘Mott transistor where the involved Mott metal-to-insulator transition can be triggered via different external perturbations, such as a gate voltage, pressure or temperature.