Despite the long title that is difficult to remember the movie itself is unforgettable. The screenplay was written by Charlie Kaufman but I heard that the actors improvised a lot, and some scenes were made up right in the place in front of the camera.
There were some of the famous actors such as Jim Carrey, Kate Winslet and Elijah Wood. I suppose you all heard at least one of the names I said. They played the main characters there. I, personally, still call Elijah Wood Frodo. I don't know why.
Anyways, let's get down to the plot. Many people would find the plot confusing and I understand why. The movie starts with the ending and then continues as real-time while going into memories. The main characters are Joel and Clementine. They meet each other on the train as if for the first time but they think they might have known each other. That is the ending... which is also the beginning. I know, it is quite confusing.
Basically what happened is that not only did they know each other but also lived together for a few years. Clementine decides to erase Joel from her memory for many different reasons. First of all she was impulsive, didn't really think about the issue deeply. Second of all, she felt quite down with him. It was like erasing some bad memories. I know, the movie is also Sci-Fi, Science fiction. You can't erase memories but in that reality you could.