The Dynamical mean-field functional renormalization group (DMF2RG) has been introduced to overcome the weak-coupling limitation of the fermionic functional renormalization group (fRG). This approach builds on the idea of exploiting the dynamical mean-field theory (DMFT) as starting point for the fRG flow, thus capturing local non-perturbative correlations via DMFT together with perturbative non-local correlations generated during the flow. We show how non-local non-perturbative correlations can be incorporated in the DMF2RG scheme by employing solutions of non-local extensions of DMFT as a starting point of the flow. The one-loop fRG flow equations are formulated within the single-boson exchange decomposition (SBE), which classifies diagrams contributing to the two-particlevertex in terms of interaction reducibility and has been proven to be a powerful bosonization scheme. We illustrate the ability of this approach to capture non-local non-perturbative correlations in the 2d Hubbard model and summarize latest methodological advances and results.