Art by Brandonjdiep on DeviantArt
In the world of Teyvat, there are seven ruling nations, each presided over by an Archon appointed by Celestia, and each having a different elemental domain. These elements include: Pyro (fire), Geo (earth), Dendro (nature), Cryo (ice), Electro (lightning), Anemo (wind), and Hydro (water).
It's narrated by a spring fairy in the book Heart of Clear Springs (II), there exist separate 'realms' for these elements, however we can infer these as elemental regions per current in-game map.
Although officially, there are 7 elements in Teyvat, that is not to say there aren't other elements, albeit unrecognized or outside the dominion of Celestia. Recent sources from Enkanomiya have hinted on primordial elements of "Light" and "Darkness".
We have also noticed Dainsleif, Lector and our sibling exhibit the ability to transcend through portals, hinting at a potential element of "Space". They also exhibit an unknown "dark" power which could potentially indicate presence of an unknown element.
There's a Nameless island near Mondstadt, as well as Thousands winds temple, where people used to worship God of Wind and Time. Hinting, there could be a potential element of "Time".
Every being with the ability to control elements makes use of one of these elements, with the Traveler being an exception, who has the capability to control Anemo, Geo, Electro and Dendro (so far). In battles, one must be mindful about combining elements accordingly, to create powerful elemental reactions which can be used to overpower one’s foes. Hence, it’s important to consider how these elements will synergize.
From the point of view of science of Teyvat, the elemental affinities of multiple wielders of the same element passively combine into Elemental Resonance, enhancing the synergies and applications of these elements.
Art by @WorldOfTeyvat (Twitter)
Some beings, mortals or otherwise, are granted what’s known as a “Vision”, which in the world of Teyvat, is seen as a gift bestowed to those who’ve been recognized by the gods. Visions grant the user the ability to manipulate and manifest the element of their given Vision. It is said that Vision holders, (also known as allogenes) have a chance at attaining godhood and ascending to Celestia (reference: dialogue with Venti).
The exact criteria on how one is chosen/granted a Vision is not yet known in-game. However, it has been hinted by the archons we've met so far, that Visions are given as a form of acknowledgement by Celestia, and that, the Archons do not have direct control over granting these out. "the key is people's desire" that resonate with their respective vision, and another aspect yet to be known.
It’s depicted that upon losing one’s vision, regardless of whether they willingly or unwillingly forfeited it, seems to have severe consequences, such as losing critical memories from the time they wielded the vision, and/or losing their ambition.
While it's rare for vision holders to possess more than one element, it's not impossible. Apart from Traveller, Kazuha has also exhibited possessing two visions of different elements simultaneously, albeit for a short period of time.
A vision seems to be comprised of roughly 3 parts:
An encasing - which is based on the region of the holder
A stone/gem: that is made of a material that seems to have the ability to resonate with elements.
The element: One out of the 7 elements recognized by Celestia.
We don't know with clarity as of yet, as to what exactly vision holders receive when receiving a vision, although it is implied in many character stories that they witnessed "a glowing ball with element" in their possession when they received their vision. Whether they receive it with the encasing or they place the encasing later is not yet known.
Upon the death of an alloegene, their Vision is rendered inactive, losing its element and thus becoming an empty husk (such as the first image above). Such Visions are known as Masterless Visions and have the chance to be re-awakened by another user by potentially resonating with the old wielder's ambition. Similar cases have been observed with Ningguang and Kazuha.