Recent advances on the log-rank conjecture in communication complexity
  The log-rank conjecture is one of the fundamental open problems in communication complexity. It speculates that the deterministic communication complexity of any two-party function is equal to the log of the rank of its associated matrix, up to polynomial factors. Despite much research, we still know very little about this conjecture. Recently, there has been renewed interest in this conjecture and its relations to other fundamental problems in complexity theory. This survey describes some of the recent progress, and hints at potential directions for future research. 
Shachar Lovett
cs.CC math.CO