I will also use this site as a location for links to the treatment of General Relativity as an Effective Field Theory (GREFT). This is a particular approach to QFT which pays attention to the low energy portion of the theory where we can make reliable predictions. Many other QFT papers are also valid in the EFT (see the Literature section), but those listed here use the EFT logic particularly.
Pedagogic introductions
The effective field theory treatment of quantum gravity. JFD – for those that know GR best but EFT less.
Introduction to the effective field theory description of gravity. JFD – for those who know EFT best but GR less.
Quantum gravity in everyday life: General relativity as an effective field theory Cliff Burgess – Living reviews
Some of JFD’s work on GREFT
General relativity as an effective field theory: The leading quantum corrections – The original paper on GREFT
Quantum gravitational corrections to the nonrelativistic scattering potential of two masses with Emil Bjerrum-Bohr and Barry Holstein. The complete calculation of the quantum correction to the Newtonian potential.
Quantum corrections to the Reissner-Nordstrom and Kerr-Newman metrics with Bjorn Garbrecht, Barry Holstein and Thomas Konstadin
Infrared behavior of graviton-graviton scattering – with Tibor Torma. Demonstrates the cancellation of IR divergences
When effective field theories fail. A talk with some possible caveats about possible boundaries of effective field theories – including comments on GREFT in the IR.
On-shell Techniques and Universal Results in Quantum Gravity with Emil Bjerrum-Bohr and Pierre Vanhove – The quantum correction via modern unitarity based methods – plus universality
Bending of light in quantum gravity and the equivalence principle with Emil Bjerrum-Bohr, Barry Holstein, Ludovic Plante and Pierre Vanhove – quantum correction to light in a gravitational field, and quantum violation of the equivalence principle
Non-local quantum effects in cosmology 1: Quantum memory, non-local FLRW equations and singularity avoidance with Basem El-Menoufi. The FLRW equations become non-local in time due to massless loops, and there are indications of singularity avoidance.
Some others that fit well in the EFT
Hawking radiation and ultraviolet regulators Burgess and Hambli – Hawking radiation in a way that makes sense in the EFT.
The Stability of flat space, semiclassical gravity, and higher derivatives Jonathan Simon. Shows that the instabilities of R+R^2 gravity lie beyond the Planck scale and then do not occur in the EFT. Cliff Burgess has a related paper.
The classical correction to the gravitational potential was calculated in QFT by Gupta and Radford. A very early work by Radkowski prefigures the EFT calculation of the quantum correction. See also this and this and this.