The emerging field of molecular electronics has brought together physicists, chemists, engineers and biologists. Large efforts on both, the experimental techniques and the theoretical methodologies, have led to fascinating developments in this field. It has been shown that the charge transport mechanisms at the molecular scale can considerably differ from those well-known in bulk solids. Phase coherent, ballistic transport as well as fully incoherent, hopping-like motion of the charge carriers may compete in determining the transport through a molecule. We review in this article basic facts related to charge transport and some of the theoretical approaches that have been developed to deal with this problem. We further show, in the special case of a DNA molecular wire, how the presence of a dissipative environment can appreciably modify the electronic spectrum of the system and thus lead to a change in its low-energy transport properties.