Quantum gravity is the long sought-after theory that will combine the theories of general relativity and quantum mechanics. Physics today is divided between these two very successful, yet contradictory theories. General relativity describes the universe on a large scale, and quantum mechanics predicts the behavior of subatomic particles on a small scale.
Previous attempts to combine these two theories by writing a quantum theory of gravity have met with infinities in the calculations that could not be removed. Quantum field theory (QFT) predicts infinities for observable quantities. In order to make sense of QFT, a procedure called renormalization must be used; this effectively means that the value of a particle's mass must be put into the theory instead of being predicted. But it turned out that this technique did not work for quantum field theories of gravity, which were all non-renormalizable.
Quantum gravity research then split into two lines of study: canonical quantum gravity and covariant quantum gravity. In canonical quantum gravity, the approach is to try to quantize the Hamiltonian formulation of general relativity. This line of research has led, for instance, to loop quantum gravity. Covariant quantum gravity used the covariant quantization methods of quantum field theory and led to different approaches, including string theory.
Today there are several different lines of research into quantum gravity being conducted. The most popular approaches are string theory and loop quantum gravity, but there are others, such as Roger Penrose's twistor theory; causal sets; causal dynamical triangulation; and more. But there is a sense among many researchers that even more radical concepts of spacetime must be formulated before quantum gravity can be written. There is also some disagreement between whether research into quantum gravity requires new radical concepts or whether attempts should first be made to reconcile the mathematical structures of general relativity and quantum mechanics.
A successful theory of quantum gravity should explain what happens at the singularities of black holes and at the singularity of our universe's Big Bang. It is expected that a final theory of quantum gravity will shed light on the nature of spacetime on a very small scale. For instance, some researchers believe that the quantum uncertainty principle will apply to the structure of spacetime. This may cause violent spacetime fluctuations which tear the very fabric of spacetime. It is also sometimes suspected that quantum gravity will reveal that spacetime has a discrete nature and that continuous spacetime is only a large scale illusion.