Is there no web-based/cloud based iTunes?

Is there no web-based/cloud based iTunes out there (think of spotify for exampe)?

With all of the "genius" ideas that Steve Jobs had, which are now lacking since he's passed on, you would have thought by now that Apple would have come up with a Music cloud based storage/library so that the songs/albums we purchase and download from iTunes won't take up the storage on our devices, but only in the cloud or on the web, and that we could log into this cloud based iTunes Library to purchase and play our music. Is it just me or does this not exist for Apple?

[Re-Titled by Moderator]