Following up on a long-standing suggestion by Aviram and Ratner, experimenters have recently made great efforts in contacting and gating single molecules. Such experiments pose new theoretical challenges not only because typical energy and length scales are different from those in conventional nanostructures such as quantum dots, but also because they involve degrees of freedom specific to molecular structures such as discrete vibrational modes or localized spins. In this talk, I will discuss several situations where the coupling to vibrational modes is predicted to dramatically affect the transport properties. Specifically, I will show that electron-vibron coupling can induce self-similar avalanche transport as well astunneling of electron pairs