Lets address the elephant in the room first. Phoenix's acting is out of this world, he takes you along with the ride & never leaves your mind for a single second.
The transition from a mentally disturbed person seeking help & coping with the atrocities of the society towards a being who is different to finally embracing the madness and becoming the mirror reflecting those same actions against their wrong doers is extremely smooth and believable.
The director is very smart to keep the ambiguity of the Joker's past still intact. You leave the cinema hall questioning a lot of things & that is the beauty of the character. People are always afraid of the unknown & that is what makes the Joker so terrifying & a formidable character who can not only go toe to toe against characters like Batman but also challenge the sanity of demigods like Superman.