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.