25 years ago - Tara Markov is born the illegitimate daughter of the king of Markovia.
20 years ago - 5-year-old Tara's geomorphic powers manifest, she is taken in to by the royal family so that Dr Helga Jace can help her control her abilities, although secretly this is done so that her more advanced metegene can be studied so that her brother Brian Markov's powers can be developed and enhanced. Her mother moves to America.
15 years ago - 10-year-old Tara is sent away by Dr. Helga Jace once her metegene has been fully mapped, sending her to America to live with her mother. She feels abandoned.
12 years ago - 13-year-old Tara Markov, tired of hiding her powers and resenting losing her place in the Markovian castle, runs away from home.
10 years ago - 15-year-old Tara, looking to become a mercenary, meets Slade Wilson. He takes her in as an apprentice, manipulating her romantic fixation on him.
Terra is a massively important character in the history of the Teen Titans, and this largely comes down to one storyline. The Judas Contract was a 1984 four-issue arc of Tales from the Teen Titans that depicted Terra, a relatively new member of the Titans but someone the readers had been reacting to positively for several years, was revealed to be a mole planted on the team by their long-time arch-enemy, Deathstroke. This storyline has been adapted several times, and is always considered a major turning point in any version of the Titans. Terra, as a character, is often overshadowed by the massive influence of this story, but she's actually a really tragic, likeable character that, when done right, is always a fan favorite.
Terra's Comic History
Terra's first appearance was in the New Teen Titans #26 in 1982, followed by her joining the team four issues later. Meanwhile her major story, the Judas Contract, was one of the first story arcs once the book was split into two separate series in 1984. While that's close enough that we could guess that Terra was always being set up to betray the team (and those early appearances become a very interesting read if you assume that was always the plan), I can't find any actual confirmation from Marv Wolfman or George Perez that she was invented specifically for this purpose. You could also read her as an innovative new character in her own right.
Tara's betrayal was a huge part of the history ot the Teen Titans, and as such it's referenced constantly. A new version of the character was even introduced in 1991, a doppelganger of the original Terra from the future. Deathstroke's problematic manipulation of the teenage Tara was retconned much later to involve some sort of mind-control serum, but a lot of the troubling parts of that relationship are left out of subsequent adaptations. There's even a third, completely different Terra with a unique look, powers and origin that often serves as a sidekick to Jimmy Palmiotti & Amanda Conner's Powergirl; an incredibly cool character that we haven't figured out how to use yet.
Our Terra Story
The Judas Contract is regularly counted among the best comic storylines ever made, and with good reason. Tara's betrayal is visceral; it's not just a betrayal of the team but a betrayal of the readers. This is the central storyline we need to adapt, and it's actually very easy to do; just put her in place, and then make that story happen. We've made it part of the sequence of events that leads to the end of that version of the team.
What we can alter a little, however, is what comes before her time with the Titans. It's already part of her story that she is the illegitimate daughter of the king of Markovia, and that after she is given her powers by Dr. Helga Jace (along with her brother, the true son of the king and heir to the throne) she's then sent away to prevent a scandal. The question I've always asked is why they brought her in in the first place? The answer, which I think works very well, is that she wasn't given the Geomorphic powers of the Markovs... she's the source. She's the one with the metagene, something that Jace mapped and then used to adapt Brian's powers. This means she's being manipulated from the beginning, and when she's sent away she's even more resentful, and prone to being manipulated by Slade into her role in one of the best stories in the history of the Teen Titans.
Because Terra is so heavily associated with one particular story in the history of the Teen Titans, attempts to create revisions of her costume tend to be attached to major retellings of that story, so there's quite a bit of pedigree to them. While her original costume was essentially just a bathing suit, the Judas Contract and the story of Terra's betrayal has been adapted both in the animated Teen Titans series and then again as a stand-alone animated movie. The first saw an extremely popular redesign that featured goggles, long hair, a black midriff-baring shirt and thick gloves and boots, a look that quickly became an internet favorite. The animated movie took elements of that design but brought it closer to the comic, keeping her short hair and domino mask while keeping the shorts. Personally, the best costume for Terra I've ever seen is the one at the top of this page. I can't find who did the artwork, but that look, with the sleeveless jacket and headphones, is just perfect.
The Problematic Stuff
So obviously, there are some issues with the Judas Contract as written that we really have to address if we're going to be responsible in the way we retell this story in our timeline. In the comic, the relationship between Tara and Slade is actually sexual, or is at least so heavily implied that it's taken as a given. That's obviously problematic as hell.
When Tara was revealed to be a mole and we saw her speaking with Slade, she was deliberately depicted in a way to make her look evil; she was smoking (clever touch) and saying things that revealed her to be a complete fake, that she actually hated all the characters that we loved. Also, she was wearing a bathrobe and flinging herself over Slade, wearing very garish glamor make-up. The intention here is probably just to make the whole thing seem WRONG, and it certainly delivers. The goal in that moment is to emphasize Tara's betrayal, to make it feel very soap-opera (which was a real strength of the Titans writing at the time). The fact that we're looking at a teenage girl and a very adult man isn't really mentioned or even part of the implied narrative there.
Later versions of this story do a much better job of showing how much of a victim Tara really is. She's a child being manipulated by a grown man. She is lonely and hurt and he's using that as a weapon against his enemies. The animated series certainly never suggested that Tara's relationship with Slade was ever sexual, and that is really the way it should stay.