He's supposed to be extremely intelligent, but a lot of writers tend to have him be a savage brute (like in the terrible Batman & Robin movie) due to not knowing what to do with him exactly after the whole Knightfall storyline.
"The hammer of justice is unisex." - Batman, Batman: The Brave and the Bold
In the comics he was very smart from the start. He spent most of his life in prison (living the sentence his father died serving) so he learned a lot about patience and he read a lot from prison. He really taught himself to survive and be the best he can be. It was the venom drug that made him much stronger but also caused his downfall. His first story was finding out that Batman is Bruce Wayne and crippling him. It was always hard for writers to try and top that so a lot of the time he'd be hopped up on the venom drug as a raving lunatic. His best stuff was in the series Secret Six (which was canceled to make way for DC's new 52 relaunch.) In Secret Six he was more of a leader and the six were all villains or antiheroes so it was a very interesting team book.