Exploiting the rich design space of organic molecules for applications in future electronic devices is one of the main challenges in nanotechnology. Several groups have recently demonstrated, for a limited set of molecules, clear single-molecule characteristics and fair agreement with computations. Now that attaching leads to individual molecules has been demonstrated we naturally enter into the next exciting phase of the research, where molecule-specific properties can be engineered and studied. The most prominent property that distinguishes organic molecules from inorganic quantum dots and nanowires is that they are floppy nano-objects with a strong coupling between charge transport and vibrational degrees of freedom (vibrons). This coupling is predicted to influence transport in dramatic ways as it may destroy the coherence of charge carriers on the molecules and can lead to strong nonequilibrium effects. Many exciting predictions have been discussed in the recent literature showing unique features of single-molecule junctions. These properties can be designed and controlled by chemists.