Once the hobbits went off with Strider, they camped out one night and wanted to hear some stories. Strider told of a story of Beren, a mortal man, who was in love with Luthien, an elven princess. He says the story does does not have a known ending. So he tells the story and Beren is slain and Luthien picks mortality.
This story is kind of what Aragorn is living since he is in love with Arwen. Tolkien does a good job of finishing the story of Beren through the life of Aragorn as we find out towards the end of the trilogy.