Finding a good theory of quantum gravity is difficult, because we currently we don't have any experimental results to test such a theory. Nevertheless, we want such a theory, because general relativity and quantum field theory, the two theories that contain basically all our understanding about the fundamental laws of physics, are incompatible with each other. Namely, general relativity is not a quantum theory, but quantum theory says that everything should be a quantum theory! See for example uncertainty principle. Superstring theory, developed by Edward Witten and other brilliant physicists is one candidate for a theory of quantum gravity. Another one is canonical quantum gravity, pioneered by Abhay Ashtekar, Lee Smolin, John Baez and others. In this theory the Palatini action of general relativity is first written in terms of the new variables of general relativity. Then canonical quantization is applied. Loop representations, or, more recently, spin networks can be used to represent the states of the theory.
There are also versions of canonical quantum gravity that
include supersymmetry. Canonical quantum gravity already makes a number of experimental predictions, although none of them can be verified with our current equipment.