A bit about quantum gravity

The quantization of gravity is one of the most important unsolved issues in theoretical physics. There are several promising avenues being pursued in this arena. These include: loop quantum gravity, causal sets, consistent discretizations etc. The problems with quantizing gravity basically all boil down to the fact that standard quantum field theoretic techniques do not work when applied to a theory like general relativity due to, among other reasons, a rather technical aspect known as diffeomorphism invariance. (This issue is more involved, and rather deeper, than the usual issue of non-renormalizability that one encounters in background dependent perturbative approaches to quantizing gravity.) Imagine doing a quantum field theory calculation where you are not allowed to say where or when things happen, at least not in any conventional sense.
Some articles on the issues of quantizing gravity (general and not too technical):
Structural issues in quantum gravity,
General lectures on quantum gravity,
How far are we from the quantum theory of gravity?,
Seth Major's page on quantum gravity,
An introduction to the quantization of gravity,
A brief history of quantum gravity,
General introduction and recent developments,
Many more articles (cataloged).
Loop quantum gravity:
Loop quantum gravity is one promising approach to a theory of quantum gravity. Being based on general relativity, it utilizes what we know about GR in the quantization scheme. Specifically, it is a theory of quantum (pseudo) Riemannian geometry which retains diffeomorphism invariance. This makes it an appealing theory, true to the spirit of relativity. It also makes the theory technically challenging to work with. However, even with these challenges, a lot of progress has been made in LQG: the gravitational source of black hole entropy has been isolated. Also, the classical black hole and big-bang singularities seem to be avoided in LQG. Perhaps the most amazing prediction of LQG is that space, near the Planck scale, is not continuous but discrete. This comes out of the theory; it is not put in "by hand".
Some articles on loop quantum gravity (fairly broad in scope):
Loop quantum gravity at Living Reviews in Relativity,
Lectures on Loop Quantum Gravity,
Quantum Geometry and Gravity: Recent Advances,
Introduction to Loop Quantum Gravity and Spin Foams,
Introduction to Modern Canonical Quantum General Relativity,
Loop Quantum Geometry: A primer,
An invitation to loop quantum gravity,
Many more articles (cataloged).