Integration with GitHub's review approval process is now live! When publishing your drafts you can now choose to comment, approve, or request changes, just like on GitHub:
Reviewable will automatically pick the appropriate state based on your discussion dispositions and file review status but you can override it as you see fit. Semantics are exactly the same as on GitHub, though Reviewable will limit you to "Comment" if you lack write permissions to the repo, since other states wouldn't be respected by GitHub anyway.
The state will count towards branch protection required reviews settings as well. Reviewable's default review completion condition remains unchanged and ignores approval states, but there's a new approval-based example in the settings editor if you want to switch to this approach. (But if all you want is the semantics provided by GitHub it's easier to just use the branch protection settings instead.)
The current approval states for all reviewers also show in the review list and the people section on the review page, so you can tell at a glance who's blocking the merge or already approved it (by icon), and whose action is needed next (by color). Note that it's not always the people requesting changes who need to take action next to move the review forward!
Finally, one feature that is unfortunately missing from this release is the publishing of native line-level comments in GitHub rather than rendering them all as part of a single top-level message. It turns out that after more than a year in production, the GitHub reviews API is still missing critical functionality to support this. See issue #437 for details if you're interested. Sorry!