TITLE: What is the Status of Borel conjecture today?
QUESTION [12 upvotes]: Let me recall the conjecture: $M$ and $N$ two aspherical closed $n$-manifolds with isomorphic fundamental groups, then $M$ and $N$ are homeomorphic.

REPLY [4 votes]: Surely the state of the art is in this paper from a few days ago at http://arxiv.org/abs/1601.00262 by some of the leading experts in the field.