Recently, substantial progress has been made in various subfields of molecular nanostructures. We list a few examples. First-principles calculations based on density-functional theory (DFT) have been successfully used for qualitative understanding of coherent transport through molecules in a strong coupling regime. However, due to inherent limitations in DFT, this approach does not provide qualitatively correct transport features for molecules where electron correlations are strong or for a weak coupling regime. Thus, in those cases, it becomes increasingly important to combine DFT with other computational and analytical tools, such as the Anderson impurity model , the dynamic mean field theory , the density matrix and the numerical renormalization group , and the GW approximation . Additionally, there has been some progress in understanding how the interactions between internal degrees of freedom of molecules and local environments affect transport characteristics. A few examples are the interplays between transport properties and vibrational [6-8] and magnetic degrees of freedom [1-3,23], spin-flip processes, adsorbate motions, dissipation, and noises. To push further developments, it is crucial to have the crosstalk among researchers pursuing these very different approaches as well as a continuous feedback from experiments.
Recent experimental progress has been highly promising. It surely motivates theorists to incorporate additional degrees of freedom into their studies and to look into new hybrid structures . Simultaneous measurements of conductance and Raman spectra for molecular junctions open a new avenue in our search for the effects of bonding geometry, chemical environments, and vibrational degrees of freedom on the transport . Experiments on break junctions reveal intriguing mechanical and collective effects [12-14]. Binding and transport properties of new hybrids and new anchor groups have been tested, including C60, with encouraging results [16-18, 21]. Low-temperature STM experiments show a possibility of controlling the Kondo effect atom by atom  and the intriguing Kondo effect for single adatoms with magnetic anisotropy . STM measurements also provide access to force constants for single adatoms  and allow to map out vibrational states of adsorbates .
Many attempts to cure the problem caused by the approximations in the DFT functionals, at least partially, are hampered by computational issues or by the necessity to keep too many degrees of freedom. A growing number of examples show how to overcome some of the difficulties by a close collaboration between experimental and computational groups. In these cases, a lack of quantitative predictability is compensated by a good understanding of qualitative trends. This positive development is partly due to (i) a better understanding of the effects of functional approximations, which is what the mathematical and analytical colleagues can take credit for, and (ii) an enhanced cooperation between the different sub-disciplines.