We're nowhere near the point of Stack Overflow with (at the time of this writing) 65.9k questions in the close queue.
I've noticed an uptick in the queue of people flagging questions. In a batch of 20, I often see a question that is not an audit that has no votes on it - this is from a flag. That's good. Increased participation is a good thing.
When it comes to the close review queue, I often see the same people doing reviews. At times, there has been a perception that only certain people close questions. Looking at the close votes of questions I have occasionally seen people who never show up in the recent reviews list.
How can we engage people to be more active in the review queues?
We can't force people to use it, and it wouldn't be the right answer even if we could. Is there a nice way to say "Hey, look, there's something here" that they were unaware of before? Or is it just that they know of it, and don't want to participate in that part of the site? Inquiring minds want to know.
Another point to consider, is that being familiar with the review page itself (even if not doing review queues) is the place where the 10k tools are located. Delete votes, site wide close and reopen votes and even the feedback from the anon and low rep reviews (see what other people are coming to the site for, what they are finding helpful or not and be able to change things (vote on answers or edit questions so that they do become more helpful)).
Considering delete votes, it takes a question to be closed for 2 days before a delete vote can be cast. This is often enough to have it fall off of the front page and so people may not be aware of this additional tool available - they'd never see the 'delete' link on the question.