There's a new paper which substantially improves lower bounds for circuit complexity. The paper, by Ryan Williams, proves that NEXP does not have ACC circuits of third-exponential size.

This is a somewhat technical result (and I haven't read the proof yet), but there's a summary of what this implies at Scott Aaronson's blog. The main upshot is that this is a substantial improvement over prior circuit complexity bounds. This is relevant since circuit complexity bounds look to be one of the most promising methods to potentially show that P != NP. These results make circuit complexity bounds be still very far off from showing that. But this result looks like it in some ways might get around the relativization barrier and natural proof barriers which are major barriers to resolving P ?=NP.