Is it OK for a grad student to do a review that their advisor was asked to do?
Pros: By doing a review, grad students are exposed to the process of reviewing (not just being reviewed).
Cons: Even if a particular student has the necessary expertise and judgment to do a review, grad students have enough to do without the extra time involved in doing a thorough review.
** I would never ask one of my students to do a review for me -- that is, instead of my doing the review. **
A few years ago, I was talking to someone at a conference who had reviewed one of my papers not long before the conference, and was horrified to find out that although he had signed the review, one of his postdocs had done the review. The review-signer hadn't even looked at the paper. I would have been fine with his postdoc doing the review and either signing or not as he wished, but I thought it was disgusting that someone had signed another person's review.
I recently involved one of my graduate students in a review, with permission from the editor, because the topic was directly related to the student's thesis topic. My student is about to graduate (Ph.D.) and had published on this topic, so I felt he was senior enough and in the right stage of his career to see what was involved in a review. In the end, 99.9% of the review comments were my own, but it was an interesting exercise for us both to read a manuscript and compare our opinions with respect to what should go in the review and how the comments should be worded to be clear and constructive. I have involved students a few other times in the past, but not often.
As an editor, I often ask postdocs for reviews. Postdocs, assistant professors, and other early-career scientists tend to do thorough and prompt reviews, though I also try not to overload any particular person with reviews just because they're a good reviewer. In general, I will ask someone for a review once/year.
2 years ago