When I was in grad school, we had a class that met once a week and talked about current research in astronomy. We were given a recently published paper to read, and then we'd discuss the methods, the results, what it meant for the field at large. It was a great way to keep up with the cutting edge work being done.
The internet has changed how a class like that can work. We used to have to wait for a paper to be physically published in a journal -- which could take up to six months after it was submitted, as was the case for a paper I worked on once (not that I'm still ticked, grrrr) -- but now once a paper is accepted by a professional journal, it can be posted online at astro-ph, a preprint database. Whenever a press release is sent out, that's one of the first places I go so I can read the details of the work leading to the release. And now some enterprising grad students at Harvard have put all this together with astrobites, a research summary blog, where they take recent papers and summarize the work. It's aimed at undergrads, but I don't see any reason it can't be used by any level of professional astronomer, from undergrad to pro. And while the level is a bit heady, I suspect a lot of folks who read my blog would find it useful as well. They don't shy away from math or complex graphs, but the posts are at different levels for different topics, and they cover a wide range of astronomical ideas. None of us is an expert in everything, so I suspect I'll spend some otherwise idle moments thumbing through the archive there. I've also added it to my feed reader. This is a very useful site, and I'm glad to see the grads at Harvard taking the initiative on it!
