The differences between story grammar and story schema are outlined and discussed based on research on story understanding by children and adults. The contention of all story grammars is that stories have a relatively invariant structure despite great differences in story content. The importance of structure within folk tales, and the ways in which children incorporate the structure into their knowledge systems, particularly comprehension and memory, are examined. These issues are addressed: finite-state versus context-free grammar, similar considerations of structure in music, ordered consitutents of a story grammar, episodes, research supporting the theory of structural knowledge guiding recall of the story, cross-cultural similarities, the influences of changes in story schema on reading times, and the effects of the structural hierarchy in stories--especially the "levels effect"--in processing. A list of references and illustrative figures are appended. (MSE)