A number of different families of nanowires which self-assemble on semiconductor surfaces have been identified in recent years. They are particularly interesting from the standpoint of nanoelectronics, which seeks non-lithographic ways of creating interconnects at the nm scale (though possibly for carrying signal rather than current), as well as from the standpoint of traditional materials science and surface science. We survey these families and consider their physical and electronic structure, as well as their formation and reactivity. Particular attention is paid to rare earth nanowires and the Bi nanoline, both of which self-assemble on Si(001).