The strange story of Harley Quinn. Creators seem to love her but never know just what to do with her. Originally she was a golden age Green Lantern villainess and love interest called Harlequin but writers on the campy 60's Batman tv show wanted to make Hugo Strange seem less terrifying and psychologically scary so they thought a wacky clown girl sidekick would tone him down some. She was a big success thanks to some excellent acting and the Batman editors decided to bring her and the new Batgirl from the show into the comics too, as archenemies. The comic writers explained that this seemingly new character was in fact Molly Mayne who'd retired from crime and was now working as a therapist to help reform criminals including one Hugo Strange, little did she know that she was being manipulated and experimented on by the criminal genius himself. Giving her a split personality each struggling for control of her body, which the criminal side won. Shortly after she'd rechristened herself as Harley Quinn, dyed her hair blonde so as to distinguish herself from Molly and donned the updated and now familiar version of her costume becoming Strange's partner in crime, to match what people had seen on the TV show.
Since then she's drifted around some, returning to the pages of Green Lantern in the Alan Scott revival era to battle him again, controlling Solomon Grundy. A constant thorn in Batgirl's side. Returning to Gotham City where a magic elixir separates Molly and Harley into two different bodies where Molly vows to bring her former alter ego to justice. This was largely so she could serve as Bruce's new love interest, only to have that relationship torn apart when they're merged together again. Mostly after that she's spent her time as Strange's hench woman and sometimes lover with not a lot of character development. The Gotham Knights mini series changed that though she was leading the Monster Men against Batman and the Alan Scott Green Lantern on her own accord the series really delved into her mental state how she was coming to the realization that she was a victim and needed to make up for her misdeeds now a mix of both the Harley Quinn and Molly Mayne personas, painted in a very sympathetic light. Mostly since then she's been an anti-hero to atone for her life of crime with a few hi-jinks filled relapses back into the dark side too in both mini-series and an on again off again ongoing solo series. Even Frenemies with Babs Gordon.
A great history even if convoluted and has the potential to become a Batman's biggest foe though that's not the direction they're going in currently. I like her inclusion in Batman's life better than say the Tigress (Paula Brooks) who was obviously a Catwoman stand in most the time.