More information has come in, so i will revise parts of the preceding post.
From Ashtekar there are several valuable surveys. Here are links to a couple of recent ones that might be useful.
http://arxiv.org/abs/gr-qc/0410054
Gravity and the Quantum
http://arxiv.org/abs/gr-qc/0404018
Background Independent Quantum Gravity: A Status Report
What is especially interesting right now is a book Ashtekar is preparing, to be published by World Scientific, called
A Hundred Years of Relativity.
This book has a broad scope covering all of General Relativity, including numerical GR and testing. It will show how Ashtekar sees LQG and allied approaches to quantizing Gen Rel in the wider context. Several chapters of this book are already online as preprints:
Martin Bojowald
http://arxiv.org/abs/gr-qc/0505057
Elements of Loop Quantum Cosmology
Larry Ford
http://arxiv.org/abs/gr-qc/0504096
Rodolfo Gambini and Jorge Pullin
http://arxiv.org/abs/gr-qc/0505023
Discrete space-time
Hermann Nicolai
["Gravitational Billiards, Dualities and Hidden Symmetries" not yet online]
Thanu Padmanabhan
http://arxiv.org/abs/gr-qc/0503107
Understanding Our Universe: Current Status and Open Issues
Alan Rendall
http://arxiv.org/abs/gr-qc/0503112
Clifford Will
http://arxiv.org/abs/gr-qc/0504086
Was Einstein Right? Testing Relativity at the Centenary