this gets very weird very fast. I'll be citing Alaric Hall's Elves in Anglo-Saxon England for my claims here, it is free to torrent on AnnasArchive so please check out that endless, dense, baffling, wonderful tome if you have a free month to spend having your brain chemistry altered by Wildly Unhinged Elf Lore.

so. the Elf (or Ælf) is a very enigmatic yet widely present entity in Anglo-Saxon culture. they are referenced most often as part of names (Ælfræd = Elf-Counciled, Ælfgifu = Elves'-Gift) where they have connotations of power and beauty, and in the names of diseases like Ælfadl (elf-sickness, no further details known) or Ælfscot (elf-shot, a sudden stabbing pain/weakness/lameness with no apparent cause, striking humans or livestock, possibly literally blamed on elves or possibly named metaphorically), or the names of poisonous or psychotropic plants such as Ælfþone (deadly nightshade). Elves are called on in charms against illness, either naming the illness as the "Elf" or calling on Elves or similar creatures to help chase the pain out of the body. Obviously none of this says much about what Elves ARE, so Hall turns to similar cultures where these traditions survived Christianization more inact. this mainly means looking Old Norse, where exactly one absolute mad bastard named Snorri wrote down every prechristian belief he could find under the guise of preserving old tales of "legendary human heroes", and at Scotland as late as the 1800s, where the failure of the Norman Conquest and its resultant Anglo-Normans to conquer Scotland allowed their shared culture with the Pre-Norman Anglo-Saxons to persist relatively unchanged by France, or by strict Continental religious oversight, for centuries.

so, what do these cultures have to say?

well, according to Hall's work, the only detailed description of Elves (Alfar) in the Old Norse record is a nearly verbatim copy of a description of Angels found in a Swedish text that Snorri (the guy who wrote all the norse stuff down, remember) would have reasonably had access to. folk belief across England, Scotland and Scandinavia (EDIT: and Ireland!) all the way up to the Victorian era back this up (see John Gregorson Campbell's various works on Fairy Tales in the Scottish Highlands for more recent accounts) (EDIT: see works of Lady Jane Wilde & contemporaries for more recent records of these traditions in Ireland), with a widespread belief that Elves and/or Fairies are, in fact

*deep, tired sigh*

....they're seen as fallen angels who were "too bad for heaven but too good for hell", and so are stuck on earth, just Elfing around I guess. if this seems like Christianization of local spirits, IT IS!

but somehow there's yet another layer to this. because Hall also records a lot of glosses (recordings of which word translates to which between different languages, especially common with harder-to-translate words such as plant names or religious/mythic concepts) for "Elf" and similar words, that show them corresponding to terms like "Nymph" or "Dryad", in the Greek sense. SO NOW ANCIENT GREECE IS INVOLVED HERE.

and now I must introduce a concept, present in both Old English and Old Norse traditions, that I like to refer to as "Schrodinger's Gigantomachia". "Gigantomachia" roughly means "Giant-fighting" in Greek, and usually refers to the battle between the Gods and the Giants in Greek (later adapted to Roman) mythology. Old English (and Old Norse) -speaking peoples had access to this story through the preservation of Greek and Roman texts by scholars in the employ of state and religious leaders such as Charlemagne, who I suppose did one good thing in his life there, and for some reason Old English and Old Norse peoples specifically LOVED Old Greek Stuff. The Anglo-Saxons (using as synonym for Old English speaking peoples here) also had access, through both descent from Nordic cultures and continued interaction with them, to the story of Odin and his brothers' slaying of the giant Ymir to create Midgard (Earth), and the subsequent battles between gods and giants throughout the Norse mythos. The Anglo-Saxons ALSO ALSO had access to, and increasingly placed sole and exclusive belief in, the Bible.

so what happened is they looked at the gigantomachia, the fights between the Norse gods (Æsir) and giants (Jotnar), and the biblical/Christain-apocrypha giants/nephilim/etc, and went "oh yeah, the time way back at the beginning of human history when God and The Heroes fought off the Giants, we've all heard of it. we've all heard of the Giant War, that's a thing that happened and all of these stories talk about it". so if you were able to go back in time and talk to an Anglo-Saxon (...or you could also just talk to me lmao, pretty close to the real thing) and you mentioned the Giant War, they would understand immediately, with that understanding being of a singular War Against The Giants that is told accurately in the Bible, and with some distortions in Greek, Roman, Norse, Pre-Christian English, and other sources (thse "distortions"- ie the presence of polytheisic deities- being blamed either on centuries/millenia of verbal transmission through non-Christian cultures, or more kindly on the natural desire of a given population to focus their retelling of the Giant War on whichever of their own Legendary Ancestors (definitely not gods) had been there).

SO.

If greek and norse myths are canon as distorted, but not totally useless or demonic, retellings of the Christian canon... and the nephilim of the bible are the giants of myth.... and Elves, being neither human nor god, are in a separate class of "other", which is notably also where Giants are categorized (see Hall again) (also see Greek nature spirits and minor natural-feature deities, which Elves were considered equivalent to, and their frequent ancestral, if not parental, ties to a Titan, Giant or other pre-Gigantomachia powerful non-olympian entity).... and if the radiant beauty of Elves is mapped onto angels, despite Elves often being malicious entities... then, naturally, Elves are seen, along with Giants, as surviving offspring of the unholy union of fallen (specifically earthbound) Angels (aside from when the Elves themselves are fallen angels of course, but in that case it does seem to be implied that they'd have children, who would be born Elves) and pre-flood human women.

and according to popular biblical apocrypha and folk belief, who were the sinful human women for whom angels fell to earth and fathered such children?

they were the daughters of Cain's line.