  Electron transmission through molecules and molecular interfaces has been a
subject of intensive research due to recent interest in electron transfer
phenomena underlying the operation of the scanning tunneling microscope (STM)
on one hand, and in the transmission properties of molecular bridges between
conducting leads on the other. In these processes the traditional molecular
view of electron transfer between donor and acceptor species give rise to a
novel view of the molecule as a current carrying conductor, and observables
such as electron transfer rates and yields are replaced by the conductivities,
or more generally by current-voltage relationships, in molecular junctions.
  In this paper I review the current knowledge and understanding of this field,
with particular emphasis on theoretical issues. Different approaches to
computing the conduction properties of molecules and molecular assemblies are
reviewed, and the relationships between them are discussed. Following a
detailed discussion of static junctions models, a review of our current
understanding of the role played by inelastic processes, dephasing and thermal
relaxation effects, is provided. The most important molecular environment for
electron transfer and transmission is water, and our current theoretical
understanding of electron transmission through water layers is reviewed.
Finally, a brief discussion of overbarrier transmission, exemplified by
photoemission through adsorbed molecular layers or low energy electron
transmission through such layers is provided. Similarities and differences
between the different systems studied are discussed.
