This review paper provides a detailed overview and critical analysis of the philosophical literature on the Rietdijk–Putnam–Maxwell argument for the four-dimensionality of the world. After briefly introducing the debate on the dimensionality of the world, I present the arguments by Rietdijk, Putnam and Maxwell, and highlight the differences between them. I subsequently raise a total of eleven objections against the Rietdijk–Putnam–Maxwell argument, and conclude that its validity is underdetermined by the formalism of special relativity.