To assist Gondry with this, he has the extraordinary Ellen Kuras as DP and Valdís Óskarsdóttir, an editor from Iceland. But it's an asset that the story doesn't start from A to Z. With a film like 21 Grams, which has a talented director and cast, the non-linear structure isn't necessary. As I mentioned, the plot is non-linear, which could've gone the wrong way if not done with skill.
And sometimes, and to the behest of the assistants of Lacuna (Kirsten Dunst, Elijah Wood, Mark Ruffalo), Joel doesn't want them all to be erased. He goes through memories they had, happy ones, sad ones, some that are just what makes up what you have emotionally with the one you've loved. So, when Joel (Jim Carrey) goes in to erase his memory of Clementine (Kate Winslet) after finding out she did just the same, he enters into a mind-warp. Enter in the concept that makes 'Eternal Sunshine' something of a un-official science fiction film - the Lacuna corporation, led by Tom Wilkinson's character, can erase just one person out of your memory, all of the experiences that you and the significant other had.
He understands, and perhaps likely experienced to a degree, what a relationship holds to- the truth, to understanding, and then when it ends, how out memory changes the relationship. But then there is also the madman genius of the current screen writing plane- Charlie Kaufman- who has written three of the most ingenious, funny, and human of "little" Hollywood movies (Being John Malkovich, Adaptation, Confessions of a Dangerous Mind). He implements a awe-inspiring blend of style to a story that is perfectly non-linear. Michel Gondry, credited as the director and co-writer of Eternal Sunshine of the Spotless Mind, is only partly responsible for the success that the film achieves.