It's primarily client-side, but React components output a virtual representation of the DOM, so it's relatively simple to render a page on the server and return HTML.

Generally you run the JSX pre-processor server-side and then everything else gets run client-side.

It's a client-side framework. You'll generally run the JSX preprocessor as part of your website's build process (i.e. before uploading it to a server).

both; either