Quantum gravity is a field of theoretical physics which seeks to develop a quantum field theory of gravitation.
Ideally, a quantum theory of gravity would reduce to ordinary quantum mechanics in the presence of weak gravitational fields, and would reduce to general relativity at large scales. It is not expected that a theory of quantum gravity would replace or invalidate general relativity. Rather, a theory of quantum gravity is expected to be to general relativity as general relativity was to Newtonian gravitation: a refinement of an existing theory which continues to serve as a useful approximation within certain limits. 
As of 2009, no satisfactory theory of quantum gravity has been advanced, and the possibility that one could be constructed remains in dispute.