She-Hulk is Jennifer Walters, cousin to Bruce Banner, better known as the incredible Hulk. Banner once sought out Jennifer, a top prosecutor in Los Angeles, in the hope that her legal expertise might help him find a solution to his plight of being pursued for the Hulk's alleged crimes - however Jen was in the midst of a case against a local crime boss, and Banner had barely arrived when Jen was badly wounded in a drive-by shooting. He had no choice but to give her a transfusion of his own blood to keep her alive long enough to reach a hospital - but, unknown to him, the gamma radiation in that blood would soon be causing Jen to transform just as he did, into a green Amazonian woman quickly dubbed 'the Savage She-Hulk'.
Okay, he maybe should have seen that coming, but give them a break - origin stories were simpler back in 1979, when Stan Lee penned the first-ever adventure of the jade giantess. Her title was quickly handed over to other writers, who - while they didn't exactly set the world on fire (the Savage She-Hulk book ended with issue #25) - developed the at-first carbon copy of the Hulk in a different direction, most notably toning down her uncontrollable rage to the point where the 'savage' She-Hulk wasn't really savage at all, just forceful and independent, in contrast to Jen's more cautious, reserved demeanour. That set the stage for the duality that exists in She-Hulk to this day - Jen and Shulkie (as she's often called, usually by her close friend Ben Grimm) aren't radically different personalities, but simply two slants on the same character: one restrained and methodical, the other free-spirited and adventurous. But as much as She-Hulk can sometimes let her impulsive nature get the better of her (she does tend to party hard), she's a far cry from her cousin's rampaging alter ego - She-Hulk (except in unusual circumstances) is an intelligent, charismatic woman, quite capable of fitting in with civilised society.
She-Hulk's original title may have folded, but that didn't keep her down - her development from a simple anger-driven brawler to a fun-loving adventuress caught the attention of other writers, and she soon found her way into the Avengers, where she became one of the team's long-standing members. She also became a member of the Fantastic Four, when - after the Secret Wars - Ben Grimm elected to remain in outer space, and chose She-Hulk to take his place on the team. She quickly settled into the FF, forming close friendships with all her teammates - including Grimm, once he returned - as well as a relationship with FF ally Wyatt Wingfoot that at one point was close enough that the pair considered marriage.
John Byrne, writer of some of the Four's most iconic adventures, including She-Hulk's tenure on the team, then made Shulkie even more prominent by launching her in a new title of her own, Sensational She-Hulk. As well as returning her to her legal roots, the title gave She-Hulk a new claim to fame: she now knew she was a character in a comic book, and regularly pulled tricks like reading her own narration captions, moving from one location to the next by jumping over the gaps between panels, punching through pages to skip ahead, and (frequently) arguing with her writer and editor about the directions storylines were going in. Byrne left the title over a creative dispute, and was replaced by a more conservative writing team, but later returned and resumed She-Hulk's madcap adventures, rounding off a sixty-issue run that cemented her status as an A-list character, and a whole lot of fun to be around.
She-Hulk continued as an Avengers member, and frequent guest star in other books - occasionally referencing her fourth-wall-breaking perception of her true nature as a comic book hero (which other characters dismissed as her talking to herself, joking, or being eccentric) - until 2004, when up-and-coming Marvel writer Dan Slott pitched a new series for her. His new She-Hulk title was a mix of comedy, action, and soap opera, with She-Hulk taking a job at Goodman, Lieber, Kurtzberg & Holloway, a law firm which was just starting a new branch specifically to deal with 'superhuman law', legal cases involving superheroes and their powers, which regular laws were frequently unable to adequately cover. Under that device, Slott poked fun at the whole nature of the Marvel world, and the strange situations that can arise in it - a newly-created superhero suing the company that allowed him to be exposed to the radiation that made him indestructible, Dr. Strange summoning a ghost to give testimony at his own murder trial, Spider-Man suing the Daily Bugle for libel, and so on. Slott's inventive way of looking at Marvel comics, as well as his seemingly-encyclopedic knowledge of its history, earned him, and She-Hulk, many new fans.
When Slott reluctantly left the book - lured away by his dream job, writing Spider-Man - he handed over the reins to none other than Peter David, renowned and much-loved author of novels and comics aplenty, including an inconic run on the Hulk. David's She-Hulk is a reinterpretation of Slott's - still comedic, but in a much more sly, witty manner, and drawing heavily on David's legendary touch for pitch-perfect dialogue. Having been betrayed by her friends (as she sees it) and disbarred from her legal practice, She-Hulk is now a cynical bounty hunter, bringing in supervillains who've skipped bail or escaped from imprisonment. Teamed with a renegade Skrull shapeshifter called Jazinda (who has plenty of issues of her own), Shulkie is slowly discovering that her own heroism can't be kept down for long.
She-Hulk currently appears in her monthly title She-Hulk (of which five trade paperbacks are available, covering all of Dan Slott's issues) as well as the six-issue miniseries The Last Defenders, in which she is convinced (in spite of her own misgivings) to be part of a revival of the Defenders team. Her original title is collected in black-and-white form in Essential Savage She-Hulk, and it and the John Byrne Sensational She-Hulk can still be found as back issues in many comic shops. A worthwhile find is Byrne's Sensational She-Hulk Graphic Novel, part of Marvel's graphic novel series, and a precursor to the Sensational series. The Fantastic Four Visionaries: John Byrne trade paperbacks include She-Hulk's membership in the team from volume five onwards, and volume three of the pre-Disassembled Avengers trade paperbacks, 'The Search for She-Hulk', focuses on her, and is a key point in her recent history. Aside from the many, many Fantastic Four and Avengers issues, there are a plethora of guest appearances in other titles to look out for - check the database at ComicBookDB for a looong list.