When to start reviewing Recently I had a few papers published, and I suppose in response to this, I received a request from Zentralblatt to be a reviewer. They ask some general questions about what I would feel comfortable reviewing, and if I would be willing to receive papers electronically. My concern about just signing up stems from the fact that I am only a second year graduate student. So my question is

When is the right time to start reviewing?

and

When did you start reviewing for journals/reviewing organizations?

Thanks ahead of time!
 A: Review whatever you feel comfortable reviewing, whenever you feel ready for it.  It's not an obligation, and the AMS Math Reviews and Zentralblatt aren't holding anything over your head.  You can refuse to review papers for all kinds of reasons -- you don't have time, you have a conflict of interest, whatever. I wrote my first review 4 years out of grad school. 
A: Reviewing is completely voluntary in all senses.  I don't know the percentage of research active mathematicians who have ever reviewed for MathReviews or Zentralblatt, but it is certainly bounded away from 100%.  It is relatively rare for a research mathematician to write reviews in any quantity over a period of more than a few years: I think it's something that many of us try out for a while but don't stick with in the long run.  For a personal touch, I am a 2003 PhD, I have written about five math reviews, and I have gotten overdue notices on about four more.  I would rather write nice, insightful reviews for half of the papers that I get sent, but I haven't yet figured out what do about that.
I agree with Tim Porter that, as a graduate student, you should discuss this with your advisor.  I think that if any of my students asked me about it, I would mildly discourage them from writing reviews, for the following reasons:
(i) It is not closely enough related to your thesis work to be a good use of a mid-to-late career grad student's time.
(ii) Prospective employers are generally not going to be more excited about your application because of the reviews you have written.
(iii) Most graduate students -- even ones who have already done some research work of their own -- don't have a broad enough perspective to write insightful reviews.  (Or, more positively put, they will have a broader perspective later on and will probably write only a bounded number of reviews in their life no matter when they start.)
Finally, I should say that refereeing papers is a totally different story.  I feel that it is an ethical (and karmic) responsibility to referee at least as many papers as one submits.  A graduate student can make a good referee for some papers, because they are less likely to feel that it is beneath them to read the paper line by line and really make sure it is correct.  
A: I actually like reviewing, and I say do it!
Reviewing forces you to read papers carefully, and to broaden your view of your field. This seems especially important when one is a grad student. I am perhaps atypical as a reviewer, in that I spend huge amounts of time reviewing papers, because it's exciting for me to see all the great work other people are doing! I know it makes me, if not a better mathematician, then at least a more widely read one. So I write maybe a few dozen reviews for Zentralblatt each year. The nasty part is when you get sent papers to review which are rubbish, in which case (I think) you do a community service by pointing out why that is so.
A: Actually, all reviews are written by research mathematicians, since MR/Zentralblatt typically only invite those who have published papers.
In fact, it is not a great burden. As everyone knows, the best way to understand some mathematics is to explain it others. If you get a paper to review that you have read, or were planning to read, then writing a review doesn't take long. If you get a paper that you weren't planning to read, then reviewing it broadens your understanding.
So my advice is to begin reviewing when invited, although no harm will be done if you prefer to wait until you are more experienced.
Since all of us benefit from reviews, all of us have an ethical obligation to contribute for at least part of our careers.
