I am wondering at what reputation the review button "comes alive".
I am happily reviewing from my Stack Overflow profile. Thought that came at 1 reputation, but guess not.
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Assuming you're talking about https://stackoverflow.com/review, the minimum reputation needed to do anything is that required for down-voting. At this level, you can review First Posts and Late Answers.
Other types of reviewing require substantially more, based on the reputation required to do something useful during the process. As shown, queues that aren't available to you yet will appear grayed out, with the reputation required noted below them.
The expectation here is that you'll spend some time learning to use the site yourself before jumping in and trying to help others.
The "review" link should already be available to you now. According to the Privileges page on New User Restrictions, this is removed at 10 reputation:
What are the new user restrictions?
New users cannot:
- post images
- post more than two hyperlinks at a time, either in a post or their user profile
- contribute answers to protected questions
- ask or answer questions too rapidly
- access the review tools
Of course, many of the features are geared towards users with at least 125 reputation:
Review allows you to monitor posts that are likely to require additional assistance from more experienced users. It is thus geared towards users with more than 125 reputation who have a better grasp of the site and its policy than a user with 10 reputation might have; the feature is, indeed, completely hidden until then.
This privilege level unlocks it, though, and you can help through editing. Look at low quality posts and see if you can propose improvements to them. Every edit suggestion will be reviewed by users with global editing privileges or more and, if accepted, will grant you 2 reputation points.
NOTE: The information on the Privileges page may need to be updated. According to Shog9, the "review" link is available at any reputation level.