The notion of link-homotopy was first introduced by Milnor in 1954, who classified 2- and 3-component links up to link-homotopy using new invariants (called mu-bar invariants) derived from the fundamental group of the link complement. The classification problem becomes much harder for more components: 4-component links were not classified up to link-homotopy for another 30 years. In 1990 Habegger and Lin found a general classification algorithm that combines Milnor's fundamental group ideas with ideas coming from braid theory. I this talk I will outline Milnor's contributions to this history with some hints as to how they fit into the general classification.