Introducing organic molecules in electronics, in general, and as active electronic transport components, in particular, is to no small degree limited by the ability to connect them electrically to the outside world. Making useful electrical contacts to them requires achieving this either without altering the molecules, or if they are affected, then in a controlled fashion. This is not a trivial task because most known methods to make such contacts are likely to damage the molecules. In this progress report we review many of the various ways that have been devised to make electrical contacts to molecules with minimal or no damage. These approaches include depositing the electronic conducting contact material directly on the molecules, relying on physical interactions, requiring chemical bond formation between molecule and electrode materials, "ready-made" contacts (i.e., contact structures that are prepared in advance), and contacts that are prepared in situ. Advantages and disadvantages of each approach, as well as the possibilities that they can be used practically, are discussed in terms of molecular reactivity, surface and interfacial science. (C) 2008 Elsevier Ltd. All rights reserved.