So I think one of the smartest things that I did as a grad student was to create an NCBI account so that I could schedule in saved weekly searches of the PubMed database. That way I don't miss the pertinent literature or have to go lurking for it, it comes straight to me. For instance, lets say you study Rump Shakin, why not follow the big whig Rump Shaka of your field, that way you can see that groovy person's new papers to determine if they are pushing the field more towards the Humpty Dance or are they skewing towards Poppin & Lockin. There are endless possibilities of searches to set up and can come to you, daily, weekly, monthly, etc, but here are some that I recommend:
-Big Whigs in the field
-Competitors (always good to know what they are putting out there)
-Your gene or protein
-Your field/subfield (I do a broad and narrow search)
-Collaborators (its sometimes nice to keep tabs on what these scalliwags are up to, when they aren't taking for damn ever to get back to you)
Hope this helps, I use this as a way to comb the literature without literally having to comb it, I just open up my inbox and the beautiful bounty of the aggregated pubs glows like the briefcase in Pulp Fiction. I'm sure many PI's do this but I have known more than a few grad students and postdocs that had no idea of this and were manually searching every week or two for topics.
I'm lazy and if "If Mohammed will not go to the mountain, the mountain must come to Mohammed," then I let the PubMed citations come to me.