I am a first year PhD student, and have been asked to peer-review a paper. The paper is not really in my field, so I will not learn anything valuable by reading the paper. The publishing venue is not open-access, so it is difficult to justify on altruistic grounds. Also, the reviews are double-blind, so there is no potential for networking. As I have never been a reviewer, I am wondering: is there any other possible personal benefits that I might realize from performing this task?
One benefit is that you are now part of the academic game and you'll learn how it's working, esp. if you have a chance to see other reviewer's comments (which is not always the case, but sometimes, all comments have to be adressed and then you can see them).
Someone might have proposed you, and this person wants to promote you.
If the paper is clearly off-topic, I would avoid reviewing it, especially if it is your first review. You should thank the editor for the trust in you, but send them a list of topics you would happliy review.
If the publication venue is a conference, you will be listed under "program committee" and gain visibility in the field.
If it is a journal: Is the journal trustworthy? I'm getting two invitations per day by some predatory journals...