A young couple discovers a cardboard baby on their stoop. They grow to love the child, who is completely flat, as their own. Then someone or something takes away the baby to a FlatWorld, a planar landscape populated by characters whimsical, sinister, and flat as pancakes. The couple, both ordinary and round, must enter this two-dimensional world to get their baby back. Can they rescue their adopted child and escape from a parallel universe in which there is up-and-down and side-to-side, but no way out?