  Electronic transport properties for single-molecule junctions have been
widely measured by several techniques, including mechanically controllable
break junctions, electromigration break junctions or by means of scanning
tunneling microscopes. In parallel, many theoretical tools have been developed
and refined for describing such transport properties and for obtaining
numerical predictions. Most prominent among these theoretical tools are those
based upon density functional theory. In this review, theory and experiment are
critically compared and this confrontation leads to several important
conclusions. The theoretically predicted trends nowadays reproduce the
experimental findings quite well for series of molecules with a single
well-defined control parameter, such as the length of the molecules. The
quantitative agreement between theory and experiment usually is less
convincing, however. Many reasons for quantitative discrepancies can be
identified, from which one may decide that qualitative agreement is the best
one may expect with present modeling tools. For further progress, benchmark
systems are required that are sufficiently well-defined by experiment to allow
quantitative testing of the approximation schemes underlying the theoretical
modeling. Several key experiments can be identified suggesting that the present
description may even be qualitatively incomplete in some cases. Such key
experimental observations and their current models are also discussed here,
leading to several suggestions for extensions of the models towards including
dynamic image charges, electron correlations, and polaron formation.
