Materials with strong electronic correlations exhibit many fascinating physical phenomena: from the Mott metal-insulator transition in V2O3 and the magnetism in Fe and Ni, to the large thermopower in CrSb2 or LiRh2O4 and the high-temperature superconductivity in some cuprates. Thus, strongly correlated materials are currently a very vivid and interesting field of research. On the theoretical side, the DFT+DMFT approach (density functional theory combined with dynamical mean-field theory), which will be introduced in the first part of this thesis, has become a well-established method over the last two decades. In this thesis, the results of a DFT+DMFT study for the magnetic properties of FeAl will be presented. While standard DFT studies fail to correctly predict the experimentally observed paramagnetism in FeAl, I show here that the absence of ferromagnetism can be explained by the correlation-induced screening of short-lived local magnetic moments of 1.6 B on the Fe site. However, even though DFT+DMFT works well for many correlated compounds, it still remains a mean-field theory in the spatial coordinates, which can capture only local electronic correlations. Thus, in order to include also non-local electronic correlations, which are important e.g. in materials with a layered 2d structure, extensions of DMFT have been developed in recent years. Among them, there is the dynamical vertex approximation (), a diagrammatic extension of DMFT. DA has already been used successfully to study model systems, in particular the one-band Hubbard model. A main part of this thesis has been the extension of DA to realistic materials - computations. This newly developed AbinitioDA method represents a unifying framework which includes both, the GW and DMFT diagrams, but also important non-local correlations beyond, e.g. non-local spin fluctuations. In the second part of this thesis, the AbinitioDA method and its numerical implementation are discussed in detail, together with the first AbinitioDA results for the transition metal oxide SrVO3.