Movies where an actor/actress gets lost in a role

I'm trying to find movies where the main character is a professional actor/actress, and in the process of trying to understand their role, they become obsessive or delusional, unable to discern reality from the production. Themes of identity and duality are in the forefront.

Obviously psychological thrillers are the preferred genre here, but I'll take satires or horror films if they also fit the criteria.

EDIT: Anybody not reading the text and just naming method actors is getting downvoted. It's two paragraphs, folks. You're not that busy.