Single-chain magnets are molecular spin chains displaying slow relaxation of the magnetisation on a macroscopic time scale. To this similarity with single-molecule magnets they own their name. In this chapter the distinctive features of single-chain magnets as opposed to their precursors will be pinpointed. In particular, we will show how their behaviour is dictated by the physics of thermally-excited domain walls. The basic concepts needed to understand and model single-chain magnets will also be reviewed.