Elizabeth hypnotically programs Simon to forget about her and also their relationship, steal a painting and bring it to her as compensation for his violent abuse of her when they were dating. Simon is killed by Elizabeth; She gets away.

Long version: 
Elizabeth (Rosario Dawson) and Simon (James McAvoy) used to date. They met when Simon sought hypnotherapy to overcome a mild online gambling addiction. The dating grows into a relationship that unleashes an envious, possessive and violent side in Simon. Simon beats Elizabeth who then dumps him; Simon stalks Elizabeth which, fearing for her life, lures Simon into a therapy session when she erases all memory he has of her and their relationship; She also programs him to gamble himself into debt; lie; steal a painting from the auction house where he works and bring it to her, apparently as compensation for his violent abusive treatment of her.

Simon hooks up with bad guys led by Franck (Vincent Cassel) to steal a 25m GBP Goya painting from the auction house. He pulls the ol' switch-a-roo but gets knocked out by Franck. Simon, stolen painting in tow, stumbles out and gets hit by a red Alfa driven by a young women. The blow unleashes the suppressed memories of Elizabeth, and Simon transferres his pent-up violence and rage towards Elizabeth at the young woman, strangling her to death. He then parks the car, stuffs his "Elizabeth" in the trunk and gives "her" the painting. Simon then slips into a coma and forgets where he put the painting.

When Simon comes to, he is contacted by Franck that has him choosing hypnotherapists to extract the location of the stolen painting from his amnesiac mind. Simon, of course, chooses Elizabeth, although he doesn't understand why. Elizabeth of course knows who Simon is and quickly puts one and two together.

After many many hypnotic sessions in which Simon is put into trances, Elizabeth helps Simon overcome his fear of being murdered by Franck and his crew by unleashing his hidden power fantasies, violent behaviour and murderous tendencies, all centered around his buried feelings for Elizabeth. During the treatment, a relationship blooms between Franck and Elizabeth, although it is unclear whether genuine feelings are involved or Elizabeth is manipulating Franck for her own survival.

Finally, Elizabeth and Simon reveal the location of the painting - in the trunk of the red Alfa Romeo, next to the decomposing corpse of the young woman. Simon tries to burn the car with Franck in it when Elizabeth rams Simon and the car into the river Thames. Simon dies, Franck escapes, Elizabeth gets away with the painting.

Elizabeth sends an interactive video message to Franck, showing him she has the painting and is enjoying it - she did not sell the painting. She gives Franck an optional message that will put him into a hypnotic trance state, presumably this will make him forget her; the film ends with him hesitating whether to open it or not.

Thanks Dan C!