As Fleming Rutledge points out, the elves were Tolkien's great invention. In Tolkien's hands, the elves were not sprites, pixies, or fairies. In The Lord of the Rings the high elves are noble, ancient, wise, immortal, powerful, and possessing great dignity. They are less magical than metaphysical, in this world but not of this world.
As has been mentioned, The Lord of the Rings lacks an overt supernatural dimension, though we have been tracking the "something else at work" that threads its way through the story, the hints and clues Tolkien drops that point us toward God. But while the story lacks an explicitly supernatural dimension, it is full of transcendence and otherworldliness. And we mainly find it with the elves. We shouldn't equate Tolkien's elves with angels, but they nudge our minds in that direction.
Rutledge draws our attention to this passage where Gandalf is describing the elves to Frodo:
"The Elves may fear the Dark Lord, and they may fly before him, but never again will they listen to him or serve him. And here in Rivendell there live still some of his chief foes: the Elven-wise, lords of the Eldar from beyond the furthest seas. They do not fear the Ringwraiths, for those who have dwelt in the Blessed Realm live at once in both worlds, and against both the Seen and the Unseen they have great power."Rutledge highlights the phrase that the elves "live at once in both worlds." That's the transcendent aspect of the elves, that they dwell both in Middle Earth and in the Blessed Realm.
As Rutledge comments, with the elves our minds are pointed toward the Christian worldview. The friends of God "live at once in both worlds," here on earth and also in the Blessed Realm.
As Philippians 3.20 says, "We are citizens of heaven, where the Lord Jesus Christ lives."
