In the last 30 years, the dynamical mean field theory (DMFT) has developed to a standard tool for the theoretical description of strongly correlated electron systems. It self-consistently maps a lattice Hamiltonian onto an impurity problem which can be solved exactly via exact diagonalization or Quantum Monte Carlo methods. In this way, all purely local correlation effects in the system are captured. However, often non-local correlations play an equally important role for correlated electron systems. In the last decade, diagrammatic extension of DMFT have emerged which take into account such spatial fluctuations by means of a Feynman diagrammatic expansion around the DMFT starting point. Unfortunately, their predictive power is limited due to intrinsic inconsistencies which lead to a violation of either the Pauli principle and/or the conservation laws of the system. In my talk, I will discuss these two problems highlighting their important implications for the predictive power of the diagrammatic extensions of DMFT. Moreover, I will discuss ideas to overcome these difficulties for the example of the dynamical vertex approximation and demonstrate their applicability for the description of antiferromagnetic fluctuations in the half-filled three dimensional Hubbard model on a simple cubic lattice.