It seems to be one of the front contenders among the Flux alternatives now. Another one is Relay/GraphQL.
Redux adheres to the basic unidirectional data flow philosophy of Flux. Where it mainly differs is that there is one store. All state is kept in a (potentially large) graph of JS objects and arrays. It is also very functional in nature.
One advantage is that it solves the Flux store singleton problem. This makes it more amenable to building isomorphic apps, among other things.
I've been using it and find that it's more straightforward than typical Flux implementations. There's less boilerplate. It also allows for more heterogeneous data storage and more flexible structure. You don't need to create a new store every time you need a new collection, for example. You can use it to store the majority of your state, and keep your React components largely stateless.