Comparative mythology has produced several confident grand theories and discarded most of them, and its history is largely the history of that discarding.
Max Muller argued in the nineteenth century that myths were misremembered descriptions of natural events, above all the sun, and that the gods were originally weather. Solar mythology dominated for a generation and then collapsed, partly under ridicule: critics showed the method could turn almost any figure into the sun, including Muller himself.
James Frazer's Golden Bough assembled an enormous comparative record around the figure of a dying and rising god and a slain sacred king. The material remains valuable and the framework does not; the examples were taken out of context from societies Frazer never visited, and the pattern was imposed rather than found.
Georges Dumezil proposed that Indo-European societies organised their myths around three functions, sovereignty, force and production, and that hypothesis has fared considerably better, though its scope is contested. Claude Levi-Strauss shifted the question from what myths mean to how they are structured, treating them as sets of oppositions worked through in variation.
Joseph Campbell's single hero pattern reached the widest audience of all and is the least regarded by specialists, on the ground that a template broad enough to fit every story cannot be evidence about any of them.
The discipline continues, more cautiously, working from documented relationships between traditions rather than from resemblance alone.