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.
Gravity and the Quantum
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:
Elements of Loop Quantum Cosmology
Rodolfo Gambini and Jorge Pullin
["Gravitational Billiards, Dualities and Hidden Symmetries" not yet online]
Understanding Our Universe: Current Status and Open Issues
Was Einstein Right? Testing Relativity at the Centenary