The central focus of this thesis is the theoretical description of non-local electronic correlations characterizing the physics of important classes of materials such as, for example, transition metal oxides or rare earth compounds. From the theoretical side, in the last two decades, a big step forward was achieved by the development of dynamical mean field theory (DMFT), which accounts, non-perturbatively, for a relevant part of the electronic correlations, namely the local ones. In that way, it was possible to theoretically understand several important effects arising in correlated materials, as the Mott metal-insulator transition. However, many fascinating phenomena such as, e.g., unconventional superconductivity or quantum criticality, originate from (or are at least strongly affected by) non-local correlations, which are not captured in the framework of DMFT. This thesis aims precisely at the development and the application of novel methods for including nonlocal electronic correlation effects at all length scales beyond DMFT. These extensions of DMFT are mostly based on the calculations of two-particle local vertex quantities. Specifically, the Dynamical Vertex Approximation (DGammaA) requires as input the local irreducible vertex (Gamma) of DMFT, and we demonstrate its applicability by analyzing the antiferromagnetic phase transition in the Hubbard model. Finally, a completely new method for considering nonlocal correlations, based on the generating functional for the one-particle irreducible vertex functions, is introduced. This novel approach, including a larger number of Feynman diagrams, might further improve over the DGammA, and, in perspective, lead to a unifying theoretical description of the nonlocal electronic correlation effects beyond DMFT.