  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.
