Eternal Sunshine of the Spotless Mind is the story of Joel Barish and Clementine Kruczynski, two lovers who decide to erase all memories of their relationship after it goes sour. We go through the erasing with Joel as well as the realization that giving up all the painful memories isn't worth giving up all the good, happy, beautiful ones. But hakuna matata - by the end of the movie, Joel and Clementine get a hold of tapes that explain the erasing and they decide to restart their relationships even though things might get just as sour as they did the first time and it's all happy glory yippy cute except a little too indie for me.
The targeted memory erasure that Joel and Clementine go through is a fictional procedure. It supposedly erases a person from your memory by tracking the places in your brain that are stimulated when you think of things related to that person.
In real life, this procedure is impossible; memories are not stored in set places in the brain, but are rather the result of a countless number of connections, stimulations, and chemicals. We know that certain organs - the hippocampus, the amygdale, etc. - are definitely involved in retaining memory, but we could never zap a certain part of them to erase a certain memory. The closest we've gotten is the drug propanolol, which blunts the memories of trama.
Poor Joel and Clementine. All that drama for a procedure that shouldn't even exist.