Quantum Gravity is the incompatibility problem caused by Quantum Theory and Relativity. One of the biggest conflicts between Quantum Theory and Relativity is the way they view the universe. Quantum Theory assumes that the universe is finite, while relativity assumes it is smooth, continous and infinite.
One theory that helped the answer the Quantum Gravity dilema is the Superstring Theory. The Superstring Theory states that a set of ten dimensions exist within our universe. These extra dimension beyond the "normal" 4 (width, depth, length, and time) help decribe not only where the particle is, but what the particle is as well as what the particle is. The Superstring Theory also adds and interesting twist to the equation though. It describes matter not as particles but as strings, tiny, little wiggling loops. By examing the particles as strings is has helped solve and patch over some interesting holes previously left by the Grand Unification Theory. Tests of the Superstring Theory have recently proved to be more conclusive and correct in predicting things like the weight of quarks. This finally plugs up the hole left by the Quantum Gravity dilemma.
The Superstring Theory describes matter as one dimensional objects as compared to the previously assumed zero dimensional point particles. And it's assumed that the mass and vibrations of these "strings" coincide with atomic spin and charge.