We review the fascinating research on charge transport through switchable molecules. In the past decade, detailed investigations have been performed on a great variety of molecular switches, including mechanically interlocked switches (rotaxanes and catenanes), redox-active molecules and photochromic switches (e.g. azobenzenes and diarylethenes). To probe these molecules, both individually and in self-assembled monolayers (SAMs), a broad set of methods have been developed. These range from low temperature scanning tunneling microscopy (STM) via two-terminal break junctions to larger scale SAM-based devices. It is generally found that the electronic coupling between molecules and electrodes has a profound influence on the properties of such molecular junctions. For example, an intrinsically switchable molecule may lose its functionality after it is contacted. Vice versa, switchable two-terminal devices may be created using passive molecules ('extrinsic switching'). Developing a detailed understanding of the relation between coupling and switchability will be of key importance for both future research and technology.