A new approach to understanding the twin paradox, based on the conventionality of simultaneity, is presented and illustrated. The canonical version of the twin paradox is discussed with reference to its historical origins and the standard explanations given for the differential aging of the twins. It is shown that these are merely specific examples of an infinite class of possible accounts, none of which is privileged. The bounds of this class are given a novel geometrical interpretation. Nonstandard versions of the twin paradox are discussed, and the conventionality of the simultaneity approach is generalized. The role of accelerated reference frames in explaining the twins' aging is also critically examined. The application of the conventionality of simultaneity to the twin paradox hopefully provides a way to settle the often discussed issue of the twins' differential aging.