Where is redux store saved?
The state in Redux is stored in memory. This means that, if you refresh the page the state gets wiped out. The state in redux is just a variable that persists in memory because it is referenced by all redux functions.
A misconception is:
In redux, we know that the state is stored as an object.
This is not correct. State in redux can be any valid JavaScript value, not just an object. It just usually makes the most sense for it to be an object (or a special object like an array) because that allows for a more flexible data structure (but you could make the state just be a number for example, according to your need).
Redux use internal memory for all data. For example, when you subscribe to Store, Redux just push listener to private array and do not use Cookies or LocalStorage.
From this part of documentation (http://redux.js.org/docs/FAQ.html#performance-state-memory) I deduce it's stored in memory, so it is not persistent.
Was just about to answer How does React and Redux store data? Is it localstorage or cookies? when it got closed as a duplicate. So I wanted to paste my answer here.
Answer
First off, it's worth noting that UI libraries don't actually manage state (other than component-level state). ReactJS and VueJS expect you to pass data to them like you would pass parameters to a function. They aren't concerned with where this data came from or how you're storing it.
Redux, on the other hand, is not a UI library -- it's a state management library. Redux does store state. The VueJS corollary to Redux would be "Vuex".
With that out of the way, the next thing you need to know is that there's a difference between state management and state persistence. Libraries like Redux and Vuex usually keep track of your variables and provide tools for changing state (reducers, specifically) - but they don't manage the persistence of that state. Persistence refers to saving the state somewhere to reload it the next time someone comes to your app - and seems to be what you're curious about (since you mentioned cookies and Local Storage)
Persistence is usually coded by hand (send the state to an API endpoint which saves it to a database, then when you reload the page you ping a different API endpoint to retrieve the state) or you utilize a plugin / module for your state manager to handle persistence for you. For example, there's a popular Redux Local Storage plugin called (trivially enough) redux-localstorage