[In ``Lecture Notes in Physics Vol. 680''. Edited by G. Cuniberti, G. Fagas, and K. Richter. Springer (2005)]
We give a brief account of the foundations, state-of-the-art, major topics, and challenges of charge transport at the molecular scale. This summary is not aiming at completeness, but rather gives an overview of what follows in the different chapters of this volume.