I say “into print”, but it is still not all the way there as it is in Atmospheric Measurement Techniques (AMT): an open-access, open-review journal. Open-access means that you can go and read it, even if you are not a member of a university with a large library and lots of journal subscriptions. By “open review” I mean that what you can see now is my un-reviewed effort; you will soon be able to see what the reviewers think of it. Once they have had their say, I will have to write a reply (which you will also be able to read) and only then produce the final copy of record. The discussion is not limited to the reviewers, either: if you have a pithy comment to make on the paper, you can go and make it. This is all very different from the traditional process whereby all the peer-reviewing happens in private and the scientific public only get to see the finished article.
It is not quite accurate to say that the paper is un-reviewed; it has been through an initial, non-public quick review. But this is mostly to filter out papers that are unreadable, on the wrong subject for the journal, or otherwise not appropriate. The serious reviewing happens over the next few weeks where you can see it happen.