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.