I just read through this incredibly illuminating thread, and here's a summary of what everyone has been able to reasonably conclude thus far, either from direct literary evidence or suggestive storytelling.
1. Long ago, the race of elves suffered in a war against humans in their original world (
#77), so with the help of
unicorns, they gained control of Ard Gaeth for inter-dimensional travel and decided to sail upon white ships and move to what is now Geralt's world/dimension. At the time this new world only had Gnomes and Dwarves.
2. Sometime after moving to Geralt's world, a faction, possibly a majority, of the elves decided to move on to a "more interesting" place. This faction became the Aen Elle, whereas the elves that stayed in Geralt's world became known as the Aen Seidhe. (
#106)
3. The two factions remained in contact and rose to prominence in their respective worlds, and all was going well for these elves for untold ages until the Conjunction of the Spheres 1500 years ago, a collision of many dimensions that also somehow broke Ard Gaeth (
#106). This makes sense as the
wiki states that the Conjunction "
trapped many unnatural creatures in this dimension, including ghouls, graveirs and vampires." It also states that humans entered the world of the Aen Seidhe via the Conjunction. It's possible that the Conjunction caused humans to enter the world of the Aen Elle as well, and that the fate of human vs. elves unraveled in opposite directions in each world.
4. Pretty bummed about losing control of Ard Gaeth, a group of especially powerful Aen Elle mages created the Hen Inchaer, the Elder Gene (
#106), in an attempt to engineer elves who can eventually recover full control of the Ard Gaeth. This gene had a peculiar feature of having an activator half and a latent half (
#106). The activator half propagates only through male lineages, the latent half only through female lineages, and the gene only becomes evident when both halves are present (
#106). This process is complicated by the fact that while one can verily receive at least half of the gene (according to one's gender), one cannot reliably receive both halves at once, as the gene split after Lara and didn't reunite until Calanthe. Sile suggests that this complicated process implies the possibility that Lara may not have been the only remaining individual with the gene, as halves of the gene may be present and undetectable in others, only to be reassembled in the future (Alvin).
5. This engineering project originated by few powerful Aen Elle, but the gene was planted among the Aen Seidhe due to the latter world's relatively brisk time (
#83). This was possible after the Conjunction because there were still a few select individuals (
Eredin,
Avallac'h,
Auberon) who could travel between the worlds of the elves, although limited by arcane devices like
Tor Zireael in Geralt's world and the Spiral in the Aen Elle's world (
#92). I assume that the Spiral is simply Tor Zireael's counterpart in the world of the Aen Elle, but we know for a fact that inside Tor Zireael are portals to other worlds, one of them leading to the world of the Aen Elle. It is interesting to note that Ciri first traveled to the world of the Aen Elle via Tor Zireael.
6. Some time after this engineering project, the Aen Seidhe
Ithlinne Aegli aep Aevenien made some prophecies, all of which has come true. Her
most famous one regarding the end of the world states that the blood of Aen Seidhe will soak the earth, and soon after there will be armed conflict, "Wolf's Blizzard" (having to do with Geralt, maybe?), and an ice age. Humans will die and the remaining Aen Seidhe will be "saved by an offspring of the Elder Blood, known also as the Swallow." Ciri's name is Swallow (
#108). This prophecy
also states that the son of Ciri will rule half the world, and her grandson will rule the whole world.
7. Emhyr wants to incestuously father a son with Ciri because he wants his offspring to rule the world. The Aen Elle wants Ciri because she's their ticket to regaining control of Ard Gaeth. Geralt and Yennefer are the only people Ciri really cares about and so they're caught up in this mess. After Ciri arrived and subsequently became imprisoned in the world of the Aen Elle (during which Eredin killed Auberon), the unicorns helped Ciri realize her innate ability to freely travel between worlds, after which she travels to the world of King Arthur, which is not in the Spiral so the Aen Elle cannot pursue her further (
#92).
8. Both Emhyr and the Aen Elle now need Geralt and Yennefer to lure her back, and as of this point, Emhyr has the upperhand because, as stated, he's a cunning motherfucker.
Let me know if I've missed anything!