The path integral formulation is one of the commonly used approaches to Quantum Gravity. It attempts to mimic the standard path-integral quantization procedure known from quantum mechanics and provide an analogical procedure for gravity within the General Relativity framework.
To define a path integral, it is customary to use discretization, which in the case of gravity takes the form of a lattice approximating the spacetime geometry. This review article gives a picture of the present stage of the efforts in this direction, including the most elaborate models, their limitations and results.