Currently the best review of LQG is this video talk:
http://loops11.iem.csic.es/loops11/i...tures&Itemid=1
The talk was given 25 May 2011 in Madrid, at the biannual Loops conference.
For a printed journal-style review try
http://arxiv.org/abs/1012.4707 which was posted in December 2010.
There is also the LQG tutorial
http://arxiv.org/abs/1102.3660