Flux is the application architecture that Facebook uses for building client-side web applications. It complements React's composable view components by utilizing a unidirectional data flow. It's more of a pattern rather than a formal framework, and you can start using Flux immediately without a lot of new code.
Flux applications have three major parts: the dispatcher, the stores, and the views (React components). These should not be confused with Model-View-Controller. Controllers do exist in a Flux application, but they are controller-views — views often found at the top of the hierarchy that retrieve data from the stores and pass this data down to their children. Additionally, action creators — dispatcher helper methods — are used to support a semantic API that describes all changes that are possible in the application. It can be useful to think of them as a fourth part of the Flux update cycle.
Flux eschews MVC in favor of a unidirectional data flow. When a user interacts with a React view, the view propagates an action through a central dispatcher, to the various stores that hold the application's data and business logic, which updates all of the views that are affected. This works especially well with React's declarative programming style, which allows the store to send updates without specifying how to transition views between states.