There are a few places you can do versioning in a REST API:
As noted, in the URI. This can be tractable and even esthetically pleasing if redirects and the like are used well.
In the Accepts: header, so the version is in the filetype. Like 'mp3' vs 'mp4'. This will also work, though IMO it works a bit less nicely than...
In the resource itself. Many file formats have their version numbers embedded in them, typically in the header; this allows newer software to 'just work' by understanding all existing versions of the filetype while older software can punt if an unsupported (newer) version is specified. In the context of a REST API, it means that your URIs never have to change, just your response to the particular version of data you were handed.
I can see reasons to use all three approaches: