How do you find out the latest news in fields other than your own?
It's always hard to follow what's happening, especially in fields other than your own. I don't have any silver bullets, just a few time tested things that require serious work.
Talk to colleagues. If you are in a research department, always go to a colloquium. MR can be used both before and after the talk to tie it with what's been going on in the area. Go to seminar talks.
Conferences. Even browsing through the list of abstracts of invited addresses at AMS Sectional Meetings helps to keep you informed. Actually attending these talks and, especially, invited addresses at the Joint Math Meetings is even better: they feature people who have been doing important work recently. I imagine other Math Societies operate in a similar way. For the past few years, the JMM has run a secion on "Current events". Like the Cambridge "Perspectives in Mathematics" conference, they make the texts of all talks available.
Browse through new books and journals and read book reviews (the ones in the Bulletin of AMS play a role similar to the MR featured reviews, but are set in a wider context). One of the biggest draws of the JMM is the book sale. By browsing through new publications, one can get the vibes of what is happening; even better, you can probe other people's reaction to anything you find interesting but don't quite understand. Bourbaki Seminar has 18 talks a year on subjects of current research interest.
I've heard that some people religiously follow all new submissions on the arXiv, but I can't vouch for the benefits or effectiveness of this method. On the other hand, once you get a wind of some new developments, you can search the arXiv for papers and surveys, many of which never make it to print in spite of being helpful (in some respects, arXiv now fulfills the role formerly played by the Lecture Notes in Mathematics).
You can run a self-teach seminar if you have at least one (ideally, 3 or more) interested colleagues. This may be on the subject of a recent paper, survey, or a book. If your colleagues are in a different field, so much the better: they can teach you what's happening there, and you can teach them something in return.
I generally subscribe to good blogs updated at a reasonable frequency from multiple fields which I think is a pretty good way to keep abreast of the news in those fields.
Here is a big list of academic blogs which might be useful.
This is partly redundant with the answer of Victor Protsak, but I want to emphasize his point 3. The main reason I am very happy that my library has many paper subscriptions to math journals is that every week I have a dozen issues to browse. When the title of an article rings a bell, I take a look at the abstract and, sometimes, it convinces me to read the introduction or at least the main theorems. For some journals, e.g. Annals of Math or Acta, I read all abstract regardless of the subject. It is not uncommon that I cannot understand a word, but still I cross nice or important results in a large portion of the mathematical subjects.
This is clearly not sufficient to adress your question, though: I had not heard of the works of Okounkov or Werner before they get their Fields medals.