Aside from the moderators, user with enough reputation* can cast votes to close and/or reopen questions. This is not a right, this is a privilege that you are being given as an active user of the community.
There is already some information about it in help, but it might be interesting to read the network-wide's Theory of Moderation. However, I feel that there are some rules that people should keep in mind when using the review queues. Some tend to be forgotten, so it's probably worth repeating them.
I'll call those the
Rules of peer reviewing on WB.
Rule 0: Be nice.
This is a general rule for the Network, but remember that the provilege you have does not make you better (or worse) than the other users and that you should try to always keep civil. And in no case, a closing vote should be used as a petty revenge.
Rule 1: Please read the post you are reviewing.
Sometimes people judge a question only by its title. The OP might have written an unfortunate title, but the question might be on-topic, not too broad, answerable, etc. Go beyond a glimpse, and really read the whole post.
Rule 2: Decide for yourself.
Do not follow trend. If a question appear in the close-review queue, it is because either someone flagged it, or someone voted to close it. But that does not mean that the question has to be closed. You are given a vote, use it fully. Do not follow the others, even if those are high-reputation users.
Rule 3: Make sure you are familiar with the scope of the site and general agreements.
I know you've probably read too much about it these days, but before voting, you should make sure that you are familiar with what is on- or off-topic on WB. As there may be some inconsistancies, seeing a similar question open isn't enough to say that the current question you are reviewing should stay open. It might be that the other should be closed as well.
One place to get started on that could be the Scope clarification discussions.
Rule 4: Don't wait until someone else starts.
Especially with lower reputation, it might be intimidating to flag a question or vote to close it if no one else did it before you. But it might simplly be that others missed that particular question. By flagging and voting on it, you'll bring it to the attention of the community. And it's ok, if people do not agree with you.
Rule 5: If you are going to vote to close and there's no comment about it on the question, take your time to write one, or refrain from voting to close.
When 5 voters agree that a question has serious problem, that question is put on-hold. Apart from closing blatantly wrong questions, one of the aim is to improve the overall quality of the questions. But that can only be done if the voters express their views. So if you are reviewing a question, make sure that there is a comment on the question that reflect your idea. If there aren't, do write one yourself.
If you can't be bothered to write a comment, don't bother voting to close, click on the "skip" button.
Rule 6: Make sure you are up to date with the discussion.
This is related to the rules 2 and 5. When the first votes to close appear and correctly commented on, it is likely that the OP will ask some details, or edit their question. So maybe that too broad vote isn't valid for the current version of the post. In any case, make sure that appart from the post, you have gone through all the comments to see what is the current standings.
Follow up on that rule, if the OP, e.g., provide a set of constraints for a broad question, make sure those are edited in the question. Either by the OP, or yourself.
Rule 7: Vote on the post, not the user.
You might have had a disagreement with the OP, or the OP is a well respected member of the community. But none of those should affect your vote.
Rule 8: Don't answer a question that you voted to close.
Seeing answers on a question, pretty much validate the question in the eyes of most. So if you vote to close a question, don't answer it, otherwise you send mixed signals.
Rule 9: If you don't like a question, but it is answerable and on-topic, downvote it, don't vote to close it.
The vote to close isn't your only tool to indicate that you are unhappy with a question. Use all your possibilities.
Thanks for reading those rules.
Note that other queues are also subjected to those rules, in particular the low-quality posts.
*: For the time being, with the beta scale still there, that would be any users with at least 500 reputation. Once the graduation process finishes, that will limit it to 3000 reputation.