How It All Got Started
Lit theorists just love to quote them some classics, and this time, they've actually got a point, because big bad Aristotle himself was one of the first people to describe narrative theory. Sure, he didn't call it that, but if you dig on into his Poetics (especially the stuff on tragedy), it's clear that he was a pioneer in narratology.
Interest in this kind of thing came and went over the centuries. Henry James, for one, wrote an 1884 essay titled "The Art of Fiction" that focused on the topic—but still, it wasn't until the twentieth century that narratology started to be fully recognized and taken seriously.
As far as its origin story goes, narrative theory owes a lot to structuralism. Structuralism lives up to its name in that it looks at a text in and of itself—it's more interested in the internal laws of the text itself than in things like author, reader, or the social environment in which the text was produced.
Structuralists get their kicks out of digging beyond a surface reading to find the main narrative devices and character types that give the text its driving force. They also look for common threads. Think of it this way: if you analyze a bunch of texts, you'll probably be able to pinpoint some specific characteristics (or patterns) that you can expect to find in them. This can help you define, say, what makes a fairytale a fairytale, or what makes a detective story a detective story. You can also look for ways in which texts depart from these templates—often for deliberate effect.
So how did narratology get started? Well, to get our answers, we need to look to the Russian formalists, an influential set of literary critics who were on the scene from the 1910s to about 1930. Formalism hones in on the form rather than the content of texts, and, like structuralism, it isn't too bothered about all that outside stuff. In fact, you could say that that formalism tries to approach literature with more of a scientific outlook.
One of the earliest and most influential theorists to approach narrative in this light was Vladimir Propp, whose massively influential work, Morphology of the Folktale, was published in 1928 and made an even bigger splash when translated into English in 1958.
By the 1960s, narratology was flourishing in France—another place where structuralism was a big deal. Bridging the geographical gap was Tzvetan Todorov, who coined the term narratology (or, as the Frenchies insist, narratologie) in 1969. Todorov was Bulgarian but did his doctorate in France under the supervision of Roland Barthes.
Todorov and Barthes, along with Gérard Genette, talked about the need for a science of narrative. Yeah, sure: literature is often seen as an arts or humanities subject, but structuralists tried to bring a scientific angle to the whole thing.
We can't talk about the early years of narratology without mentioning one more theorist: Claude Lévi-Strauss. This guy was an anthropologist and so didn't just limit himself to literary criticism, but his focus was always the same: he was all about uncovering structures. Travelling around the world and getting familiar with the stories that people told in places as far-flung as the Amazonian jungle, Lévi-Strauss came to the conclusion that, despite some surface differences, these stories often shared a common structure and used the same sorts of narrative devices.