One is a world-weary music aficionado, Adam (Tom Hiddleston) and his wife of many centuries. Eve (Tilda Swinton). The roles are cast perfectly in the film. Swinton always seems otherworldly but Hiddleston is the one given the most opportunity to develop a character. He is immortal but he wants to be done with it all. He lives in Detroit, a perfect zombie hide out if there ever was one. Adam is also a music enthusiast. He listens, he collects instruments and he records his own dreary, darkwave-esgue psych rock.
This is a fantasy life for many musicians; he has no worry about money, he has all the gear he could want and he creates music people trade like it was a drug. The only down side for him is that these same humans (or "zombies" as he names all those with a pulse) seek him out.
But it isn't enough. There is something missing and it is, in part, Swinton but his ennui is due to more than just his beloved being half way around the world.
Some will walk out perplexed. The film alludes to many possible stories and it explores and concludes virtually none of them. It is sort of like most people's lives. Maybe this is a parable about how, even if we lived eternally we would still have the same angst we have as mortals. We would still leave so much unfinished even if we had forever.
It is a thoughtful, slow paced, dark film with a wry sense of humor. There is no hilarity here at any point but a sort of low key irony. John Hurt, Mia Wasikowska and Anton Yelchin (Mr. Chekov in the new Star Trek films) all add to the film in small roles. Yelchin's Ian is sort of Adam's Renfield in the movie but he doesn't procure virgin blood but vintage guitars. Wasikowska is a fly in the ointment, Swinton's "sister" who shows up to mess things up.
You want to see more of these characters. You never will. But you can feel free to create the rest of the story on your own. This isn't "typical Jarmusch," if there is such a thing. It is a film that shows a director still growing and changing after decades of work.