Is there a backstory for Batman and the Joker? How far does it go?

In the theatrical cut of Suicide Squad, the Joker and Batman have no interactions. However, given their history from the comics, they must know each other. Right? I wouldn’t be surprised if the Dark Knight was the one who captured the Clown Prince of Crime in the first place.
However, it isn’t clear how well these two characters know each other in the DCEU, if at all. All we know is that Batman did chase, at one time, the Purple Lamborghini. And that is about all. And this chase happened after the death of Robin.
However, there needs to be more than this, in order to establish the Joker as Batman’s nemesis. So how long a career does the Ace of Knaves have? How many times did he clash with the Dark Knight? Did he escape more than once from Arkham? Was Harley really his accomplice when he killed Robin?
So many questions – and the future DCEU movies must find the way to answer them!
