Theta-Delta is the most widely used symbol in representing Therianthropy. The symbol consists of two Greek letters layered on top of each other: the Delta and the Theta characters. Both characters are typically depicted in the same color against a contrasting single color background, and may be styled further by intertwining the letters.
Were/Therian Symbol History
There have been a few attempts to create a symbol for Therians. On August 17, 1999, BleuLynx announced a Weresymbol contest through AHWW.  In November of 1999, Kamatu announced voting for an International Weresymbol and links to a now defunct website known as The Changing Times. Unfortunately, the page with the symbols was not archived, so we are unable to see the designs.  
The Theta-Delta was created in 2003 on an early version of The Werelist forums. The intent was to make a universal Therian symbol for the entire community, and after considering various ideas, the Theta-Delta was selected.
It was a joint effort between the WereList and then popular Awereness forums (aka TO Forums). There was another user on the TO forums that was a fellow artist, I *think* his name was Crinos but I can't recall if I'm just mixing up WWtA stuff with this guy. Anyway, he and I put the logo together. There was a lot of people involved in giving suggestions though, so it wasn't just us. I just recall our contributions better than what others suggested. I suggested a mix of triangle, which stood for change, and a circle which stood for equals. The reason we didn't want pawprints and stuff is that is very alienating for non-canine/feline/blah blah therians. But two non-species specific symbols would work out better.
Crinos was the one that put the circle in the triangle. And then I believe that Coyote Osborne was the one that suggested we make it an official greek "theta-delta" so that at least the symbology was somewhat "normal" (Hey, it's two greek letters) and because Therianthropy's root word of origin (therios) is greek AND started with the Theta.
It all came together so well, and it was really the first time the majority of the werecommunity ever agreed on anything (There was a lot of animosity towards other sites back in those days). So it was pretty well received and still used to this day."
The symbol was seen as appropriate due to a number of reasons, including logo simplicity and appropriate symbolism. Theta, being a T, represented the word "Therian" and Delta represented change, as in a shift. (citation needed). Unfortunately the original forum thread disappeared in a server crash a few months later and nearly all the web pages explaining the theta-delta symbol were lost, having not been archived. We do know that a Werelist member made a web page detailing the Theta Delta logo, distributing image files to be customized and used freely.
One of its original uses was to be optionally worn, as an identifying symbol, so that other Therians would recognize the wearer as another Therian, and not feel awkward about starting a conversation about Therianthropy.
Today, we see many adaptations of the basic design across the internet. The symbol is often turned into unique charms with personal significance to the person wearing it.
This version of the symbol was created by Slavasesh between 2015-2016.
"The green symbolizes beings of the land, blue those of water, and white those of flight, or in the air. The black symbolizes the unknown, AKA the reason we feel the way we do."
Historical Symbolism & Meanings
Delta (uppercase Δ, lowercase δ; Greek: Δέλτα [ðelta: Dhelta]) is the fourth letter of the Greek alphabet. In the system of Greek numerals it has a value of 4. Delta was derived from the Phoenician letter Dalet, and in the Ancient Greek language it represented a voiced dental plosive /d̪/. The upper-case letter Δ often denotes difference and can symbolize a change.
Theta (uppercase Θ, lowercase θ or ϑ; Greek: Θήτα [Theta]) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth. In has a value of 9 in the Greek numeric system.
"Theta-Delta Symbol" Werelist Archive, 2008. http://www.werelist.net/archive/index.php/t-15250.html
- ↑ https://groups.google.com/forum/?hl=en#!searchin/alt.horror.werewolves/weresymbol%7Csort:relevance/alt.horror.werewolves/F14KE9Ep4Zg/HVCQrrvRHFkJ
- ↑ AHWW, November 5, 1999. https://groups.google.com/forum/?hl=en#!searchin/alt.horror.werewolves/therianthrope%7Csort:date/alt.horror.werewolves/Hogb5DAPLDA/Lx15fCNgKC4J
- ↑ The Changing Times, January 6, 2000. (archived page) https://web.archive.org/web/20000106232627/http://www.thechangingtimes.com:80/
- ↑ http://www.werelist.net/archive/index.php/t-32006.html