Double-hybrid density functionals: merging wavefunction and density approaches to get the best of both worlds

We review why and how double-hybrid density functionals have become new leading actors in the field of computational chemistry, thanks to the combination of an unprecedented accuracy together with large robustness and reliability. Similar to their predecessors, the widely employed hybrid density functionals, they are rooted in the Adiabatic Connection Method from which they emerge in a natural way. We present recent achievements concerning applications to chemical systems of the most interest, and current extensions to deal with challenging issues such as non-covalent interactions and excitation energies. These promising methods, despite a slightly higher computational cost than other typical density-based models, are called to play a key role in the near future and can thus pave the way towards new discoveries or advances.