What are some economic models of the oligopoly market structure?

So I know we have that general model of a competitive market, and the one of a monopoly, both of which we learn in our econ 101 classes which form the basics. I'm wondering, what models are there for a oligopoly market structure, such as The Cartel Model. My bigger question is, given we've come up with general models for competitive markets and monopolies, how come we don't have general models for monopolistic competition or oligopolies?