Though Cohen has been coy about many of the song's lyrics, he has said in several interviews that the song's title, "Famous Blue Raincoat," actually refers to a specific raincoat he used to own. In the liner notes to The Best of Leonard Cohen (1975), he says that he brought the raincoat in 1959 at a Burberry store in London. The woman he was with at the time didn't like it, though he claims, "it hung more heroically when I took out the lining, and achieved glory when the frayed sleeves were repaired with a little leather." He kept the coat for more than a decade, until it was stolen in the early 1970s.
In a 2008 interview on NPR's Fresh Air, Cohen remembered how the fancy coat seemed to embody the promise of an elegant future that awaited him—a future that he never completely realized. In the song, the coat gets shifted from Cohen's shoulders to those of his betrayer, but the theme is the same: youthful dreams that eventually dissolve with time. And dreams, unlike frayed coat sleeves, cannot simply be patched over with a bit of leather.