The relation between myth and ritual is among the oldest problems in the study of religion, and the positions taken on it have structured much of the field.
The myth-and-ritual school, associated with William Robertson Smith, James Frazer, Jane Harrison and the Cambridge Ritualists, and later with S. H. Hooke's work on the ancient Near East, held that myth and ritual are two aspects of a single thing, myth being the spoken correlate of the rite, the text of what is enacted. In its strong form, advanced by Hooke and the pattern theorists of the 1930s, it claimed a common ritual pattern across the ancient Near East centred on divine kingship and the new year, with the myths serving as its libretti. Lord Raglan pressed the priority claim furthest, holding that all myth derives from ritual.
The strong version has not survived. Many myths have no known corresponding ritual and many rituals have no myth. The ancient Near Eastern "pattern" was assembled by generalising from a thin evidence base and reading gaps in one culture's record from another's. And the priority claim is unfalsifiable in most cases, because the origins of both are unrecoverable. Clyde Kluckhohn's assessment of 1942, that the two are frequently but not universally connected, and that neither can be shown to be generally prior, is close to the field's settled position.
The alternatives are several. Ritualists hold that ritual is prior and myth secondary. Mythologists, including much nineteenth-century nature-mythology and Max Muller's philological approach, hold that myth is prior and ritual its enactment. Functionalists such as Malinowski held that myth is a charter validating existing institutions and practices, without requiring any ritual origin at all, his formulation, that myth is a social charter rather than an explanation, remains widely used. Structuralists, and Levi-Strauss above all, treated myth as a system for handling conceptual oppositions and were largely uninterested in ritual as its source.
What survives from the school is the observation that myth and ritual very often do illuminate one another, and that studying either in isolation from practice is a mistake, an insight that shaped the field permanently even after the theory carrying it was abandoned. The recitation of the Enuma Elish at the Babylonian new year, the Passover Haggadah's narration embedded within the meal it explains, and the Christian eucharist's rehearsal of a narrative within the act it institutes are genuine instances of the connection. It was the generalisation from such cases, rather than the observation of them, that failed.