What are the benefits of serving as a reviewer, initially as a PhD/PostDoc and later as a faculty member/research scientist? The very first thought that comes to mind is that reviewing a paper is like giving back to the academic community. After all, one's own work is published after the efforts of some anonymous reviewer. 

But what are the primary incentives that motivate so many researchers to voluntarily serve as reviewers? Does it make a researcher more established/reputed? How does it differ in the case of PhD students as opposed to faculty members?
The primary advantage of peer reviewing is that you are ahead of the researchers in your field by a margin of several months. Second advantage of getting a bad paper for review is that you get an idea "what to avoid" in your own future work. Most people do not realize this because it is not a paid service, nor there is any public acknowledgement on the paper. Several journal editors have mentioned to me that they have difficulty inviting reviewers. I asked an editor of a pretty good review-type journal and he mentioned that at times he has to write to 10-12 people and only a few respond. It is a also common complaint among editors that people from certain countries don't commonly accept peer review requests because the academic promotion is based on paper publications rather than article reviewing.

In short, we should accept review requests, if we feel we are qualified to do so, as a service to the community as well for your own education.