When should I add Redux to a React app?
React is a UI framework that takes care of updating the UI in response to the “source of truth” that is usually described as a state “owned” by some component. Thinking in React describes the React state ownership concept very well, and I strongly suggest you go through it.
This state ownership model works well when the state is hierarchical and more or less matches the component structure. This way the state gets “spread out” across many components, and the app is easy to understand.
However sometimes distant parts of the app want to have access to the same state, for example, if you cache fetched data and want to consistently update it everywhere at the same time. In this case, if you follow the React model, you’ll end up with a bunch of very large components at the top of the component tree that pass a myriad of props down through some intermediate components that don’t use them, just to reach a few leaf components that actually care about that data.
When you find yourself in this situation, you can (but don’t have to) use Redux to “extract” this state management logic from the top-level components into separate functions called “reducers”, and “connect” the leaf components that care about that state directly to it instead of passing the props through the whole app. If you don’t have this problem yet, you probably don’t need Redux.
Finally, note that Redux is not a definitive solution to this problem. There are many other ways to manage your local state outside the React components—for example, some people who didn’t like Redux are happy with MobX. I would suggest you to first get a firm understanding of React state model, and then evaluate different solutions independently, and build small apps with them to get a sense of their strengths and weaknesses.
(This answer is inspired by Pete Hunt’s react-howto guide, I suggest you to read it as well.)
I've found that the ideal path for adding Redux to an application/stack is to wait until after you/app/team are feeling the pains that it solves. Once you start seeing long chains of props
building up and being passed down through multiple levels of components or your finding yourself orchestrating complex state manipulations/reads, that could be a sign that your app may benefit from introducing Redux et al.
I recommend taking an app that you've already built with "just React" and see how Redux might fit into it. See if you can gracefully introduce it by plucking out one piece of state or set of "actions" at a time. Refactor towards it, without getting hung up on a big bang rewrite of your app. If you're still having trouble seeing where it might add value, then that could be a sign that your app is either not large or complex enough to merit something like Redux on top of React.
If you haven't come across it yet, Dan (answered above) has a great short-video series that walks through Redux on a more fundamental level. I highly suggest spending some time absorbing pieces of it: https://egghead.io/series/getting-started-with-redux
Redux also has some pretty great docs. Especially explaining a lot of the "why" such as http://redux.js.org/docs/introduction/ThreePrinciples.html